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the popular hierarchical model of galaxy formation predicts that elliptical galaxies found today in the cores of rich clusters formed at high redshifts and at rare high - density peaks of the dark matter distribution . within these regions , gas - rich proto - galaxies merge together rapidly , forming stars at a high rate . the same reservoir of gas used to build the stellar mass can also fuel the growth of the supermassive black holes ( smbh ) found dormant in the centre of the galaxies at low redshift ( e.g. kauffmann & haehnelt 2000 ; page et al . 2001 ; hopkins et al . 2008 ) . since massive star formation is known to be a dusty phenomenon , the optical light from many young galaxies should be highly obscured . dust enshrouded star formation is , however , a luminous phenomenon in the millimetre through far - infrared wavebands where the star - light absorbed by dust grains is re - emitted . indeed , in the last decade , deep surveys at submillimetre ( e.g. smail , ivison & blain 1997 ; hughes et al . 1998 ; eales et al . 1999 ; scott et al . 2002 ; coppin et al . 2006 ) and millimetre ( e.g. greve et al . 2004 ; bertoldi et al . 2007 ) wavelengths have identified a high - redshift population of massive , dusty galaxies that are undergoing extreme starbursts ( e.g. smail et al . . likewise , hotter dust heated in the circumnuclear environment of an agn will emit at mid - infrared wavelengths . therefore , submillimetre and mid - infrared observations can be combined to study activity in forming galaxies due to dust obscured starbursts and agn .    to - date there has been no published survey at ( sub)millimetre or far - infrared wavelengths of a randomly selected region of sky over an area sufficiently large to ensure that very rare structures in the early universe are contained within it . although large surveys of this type will be available soon from instruments such as scuba-2 on the jcmt and spire / pacs on - board the _ herschel space observatory _ , published surveys have so far been limited to an area of @xmath9  deg@xmath10 ( coppin et al . 2006 ; austermann et al . 2010 ; wei et al . one of the largest published submillimetre surveys is the scuba half - degree extragalactic survey ( shades ; mortier et al . 2005 ; coppin et al . 2006 ) which , due to technical problems , mapped only 0.2 deg@xmath4 discovering @xmath11 submillimetre galaxies ( smgs ) . whilst this survey provided one of the largest and most uniformly selected samples of smgs ever assembled , the area of sky surveyed is extremely small by most standards . for example , @xmath12cdm simulations predict that a dark matter halo of mass greater than a few times @xmath13  m@xmath14 at @xmath15 will evolve to become a very rich cluster of galaxies by @xmath16 ( e.g. farrah et al . 2006 ) . however , since the surface density of such massive haloes at @xmath17 is only of order @xmath18  deg@xmath10 ( evrard et al . 2002 ) , a wide - area survey would be required in order to contain one by chance .    one promising method of locating rare structures is to target the fields of high - redshift active galactic nuclei ( agn ) . given their huge luminosities , such objects must contain a smbh even at very high redshifts , and therefore must represent some of the most massive objects in existence at their epochs . they should thus act as signposts to rare high - density regions of the early universe , and can be observed efficiently with existing technology . several groups have exploited this technique to search for proto - clusters forming around high - redshift radio galaxies ( e.g. kurk et al . 2000 ; pentericci et al . 2000 ; ivison et al . 2000 ; stevens et al . 2003 ; smail et al . 2003 ; de breuck et al . 2004 ; greve et al . 2007 ; venemans et al . 2007 ) and quasi - stellar objects ( qsos ; stevens et al . 2004 ; priddey , ivison & isaak 2008 ) . most of these studies have concentrated on extreme objects , those with the highest luminosities and at the highest redshifts , and all have found over - densities of star - forming galaxies ( typically ly@xmath19 emitters or smgs ) in the fields of the agn . here we extend this work to investigate the environments of typical qsos at submillimetre and mid - infrared wavelengths . the qsos are selected over the redshift range @xmath0 where the star - formation rate density and accretion luminosity density of the universe peak . this work is motivated by the desire to study the coupled formation of stellar mass and black holes in galaxies that should evolve to become typical ellipticals in moderately rich clusters by the present day . since the bulk of the field smg population are also found at these redshifts ( chapman et al . 2003 , 2005 ) we can also compare the properties of galaxies found in different environments . this paper presents submillimetre and mid - infrared imaging data for 5 qso fields . we extract submillimetre catalogues and integral number counts , and compare these with results from blank field surveys . we then characterise the mid - infrared properties of the qsos and the smgs discovered in their fields . a hubble constant @xmath20  kms@xmath21mpc@xmath21 and density parameters @xmath22 and @xmath23 are assumed throughout . [ cols="<,^,^,^,^,^ " , ]     ( 8.0,3.0 )    ( 7.0,3.0 ) likely mid - infrared counterparts to the submillimetre galaxies are given in table  [ table : spit ] . for each field we searched within fixed radii of the extracted submillimetre positions . these radii of 5 arcsec at @xmath24 and @xmath25 m , and 10 arcsec at @xmath26 m were chosen to approximately match the theoretical error circles on the submillimetre positions added in quadrature with the uncertainty on the mid - infrared positions , which are significant at @xmath26 m ( see ivison et al . 2007 for a full discussion ) . the corrected @xmath27 statistic ( downes et al . 1986 ) is given for each source found within the search radii . this quantity is given by @xmath28 $ ] where @xmath29 , @xmath30 , @xmath31 is the search radius , @xmath32 is the surface density of objects at the limiting flux density of the catalogue , @xmath33 is the surface density of objects brighter than @xmath34 where @xmath34 is the flux density of a potential counterpart galaxy located a distance , @xmath35 , away from the submillimetre position .    a value of @xmath36 is typically used as a threshold to select robust radio ids ( e.g. ivison et al . 2002 , 2007 ) to submillimetre galaxies . we select all mid - infrared sources found within our search radii as potential counterparts and use the @xmath27 statistic to distinguish between competing ids when more than one galaxy is found . we note that almost all smgs listed in table  [ table : spit ] have mid - infrared counterparts for which the computed @xmath27 value is @xmath37 in at least one waveband , and can therefore be considered robust based on this criterion . the 4 qsos detected at submillimetre wavelengths have counterparts in all 3 _ spitzer _ bands . in addition , we find counterparts in at least one waveband for @xmath38 per cent of the smgs . postage stamp images of the mid - infrared counterparts are shown in figs  [ fig : post1 ] and [ fig : post2 ] which can be found in appendix a.    lcccccccclfield & i d & @xmath39 & cat # & @xmath40 & ra & dec & @xmath41 & @xmath27 & note + & & ( @xmath2 m ) & & ( @xmath2jy ) & ( j2000.0 ) & ( j2000.0 ) & ( arcsec ) & + rxj@xmath42 & @xmath43 & @xmath24 & @xmath44 & @xmath45 & @xmath46 @xmath47  @xmath48 & @xmath49  @xmath50 @xmath51 & @xmath52 & @xmath53 & qso + [ 1pt ] & @xmath43 & @xmath54 & @xmath55 & @xmath56 & @xmath46 @xmath47  @xmath57 & @xmath49  @xmath50   @xmath51 & @xmath58 & @xmath59 & qso + [ 1pt ] & @xmath43 & @xmath60 & @xmath61 & @xmath62 & @xmath46  @xmath47  @xmath63 & @xmath49  @xmath50  @xmath64 & @xmath65 & @xmath66 & qso + [ 1pt ] & @xmath67 & @xmath24 & @xmath68 & @xmath69 & @xmath46  @xmath47  @xmath70 & @xmath49  @xmath50  @xmath71 & @xmath72 & @xmath73 & + [ 1pt ] & @xmath67 & @xmath54 & @xmath74 & @xmath75 & @xmath46  @xmath47 @xmath76 & @xmath49  @xmath50  @xmath77 & @xmath78 & @xmath79 + [ 5pt ]    rxj@xmath80 & @xmath43 & @xmath24 & @xmath81 & @xmath82 & @xmath83 @xmath84  @xmath85 & @xmath86  @xmath87 @xmath88 & @xmath89 & @xmath59 & qso + [ 1pt ] & @xmath43 & @xmath54 & @xmath74 & @xmath90 & @xmath83  @xmath84  @xmath91 & @xmath86  @xmath87  @xmath92 & @xmath93 & @xmath94 & qso + [ 1pt ] & @xmath43 & @xmath60 & @xmath95 & @xmath96 & @xmath83  @xmath84  @xmath97 & @xmath86  @xmath87  @xmath98 & @xmath99 & @xmath94 & qso + [ 1pt ] & @xmath100 & @xmath24 & @xmath101 & @xmath102 & @xmath83  @xmath84  @xmath103 & @xmath86  @xmath104  @xmath105 & @xmath106 & @xmath107 & + [ 1pt ] & @xmath100 & @xmath54 & @xmath108 & @xmath109 & @xmath83  @xmath84  @xmath110 & @xmath86  @xmath104  @xmath111 & @xmath112 & @xmath113 & + [ 1pt ] & @xmath100 & @xmath60 & @xmath114 & @xmath115 & @xmath83  @xmath84  @xmath116 & @xmath86  @xmath104  @xmath117 & @xmath118 & @xmath119 & + [ 1pt ] & @xmath120 & @xmath24 & @xmath121 & @xmath122 & @xmath83  @xmath84  @xmath123 & @xmath86  @xmath124  @xmath125 & @xmath126 & @xmath127 & + [ 1pt ] & @xmath120 & @xmath54 & @xmath128 & @xmath129 & @xmath83  @xmath84  @xmath130 & @xmath86  @xmath124  @xmath131 & @xmath132 & @xmath73 & + [ 1pt ] & @xmath133 & @xmath24 & @xmath134 & @xmath135 & @xmath83   @xmath84  @xmath136 & @xmath86  @xmath87  @xmath137 & @xmath138 & @xmath139 & + [ 1pt ] & @xmath133 & @xmath24 & @xmath140 & @xmath141 & @xmath83   @xmath84  @xmath142 & @xmath86  @xmath87  @xmath143 & @xmath144 & @xmath145 & + [ 1pt ] & @xmath133 & @xmath54 & @xmath146 & @xmath147 & @xmath83  @xmath84 @xmath148 & @xmath86  @xmath87   @xmath149 & @xmath150 & @xmath151 + [ 1pt ] & @xmath133 & @xmath54 & @xmath152 & @xmath153 & @xmath83  @xmath84 @xmath154 & @xmath86  @xmath87  @xmath143 & @xmath144 & @xmath155 + [ 5pt ]    rxj@xmath156 & @xmath100 & @xmath24 & @xmath157 & @xmath158 & @xmath159 @xmath160  @xmath161 & @xmath162  @xmath163 @xmath164 & @xmath165 & @xmath113 & + [ 1pt ] & @xmath100 & @xmath54 & @xmath166 & @xmath167 & @xmath159  @xmath160  @xmath161 & @xmath162  @xmath163  @xmath168 & @xmath169 & @xmath119 & + [ 1pt ] & @xmath100 & @xmath60 & @xmath114 & @xmath170 & @xmath159  @xmath160  @xmath171 & @xmath162  @xmath163  @xmath172 & @xmath173 & @xmath94 & + [ 1pt ] & @xmath174 & @xmath24 & @xmath175 & @xmath176 & @xmath159  @xmath160  @xmath177 & @xmath162  @xmath163  @xmath178 & @xmath179 & @xmath180 & + [ 1pt ] & @xmath174 & @xmath54 & @xmath181 & @xmath182 & @xmath159  @xmath160 @xmath183 & @xmath162  @xmath163  @xmath184 & @xmath185 & @xmath186 + [ 1pt ] & @xmath187 & @xmath188 & @xmath1 & @xmath189 & @xmath159  @xmath160  @xmath190 & @xmath162  @xmath163  @xmath191 & @xmath192 & @xmath193 & likely false i d + [ 5pt ]    rxj@xmath194 & @xmath43 & @xmath24 & @xmath195 & @xmath196 & @xmath197  @xmath198  @xmath199 & @xmath200  @xmath201 @xmath202 & @xmath203 & @xmath204 & qso + [ 1pt ] & @xmath43 & @xmath54 & @xmath205 & @xmath206 & @xmath159  @xmath198 @xmath207 & @xmath200  @xmath201  @xmath208 & @xmath209 & @xmath204 & qso + [ 1pt ] & @xmath43 & @xmath60 & @xmath1 & @xmath210 & @xmath159  @xmath198  @xmath211 & @xmath200  @xmath201  @xmath212 & @xmath213 & @xmath94 & qso + [ 1pt ] & @xmath174 & @xmath24 & @xmath214 & @xmath215 & @xmath159  @xmath198 @xmath216 & @xmath200  @xmath217  @xmath218 & @xmath219 & @xmath220 & + [ 1pt ] & @xmath174 & @xmath24 & @xmath221 & @xmath222 & @xmath159  @xmath198 @xmath223 & @xmath200  @xmath217  @xmath224 & @xmath225 & @xmath226 & + [ 1pt ] & @xmath174 & @xmath54 & @xmath227 & @xmath228 & @xmath159  @xmath198 @xmath223 & @xmath200  @xmath217  @xmath229 & @xmath230 & @xmath231 & + [ 1pt ] & @xmath187 & @xmath24 & @xmath232 & @xmath233 & @xmath159  @xmath198 @xmath234 & @xmath200  @xmath201  @xmath235 & @xmath118 & @xmath236 & + [ 1pt ] & @xmath187 & @xmath54 & @xmath237 & @xmath238 & @xmath159  @xmath198 @xmath239 & @xmath200  @xmath201  @xmath240 & @xmath241 & @xmath242 & + [ 1pt ] & @xmath67 & @xmath24 & @xmath243 & @xmath244 & @xmath159  @xmath198 @xmath245 & @xmath200  @xmath217  @xmath246 & @xmath247 & @xmath248 & + [ 5pt ]    rxj@xmath249 & @xmath43 & @xmath24 & @xmath250 & @xmath251 & @xmath252 @xmath253  @xmath254 & @xmath255  @xmath256 @xmath257 & @xmath258 & @xmath259 & + [ 1pt ] & @xmath43 & @xmath54 & @xmath260 & @xmath261 & @xmath252  @xmath253  @xmath254 & @xmath255  @xmath256  @xmath262 & @xmath263 & @xmath264 & + [ 1pt ] & @xmath43 & @xmath60 & @xmath265 & @xmath266 & @xmath252  @xmath253  @xmath267 & @xmath255  @xmath256  @xmath268 & @xmath269 & @xmath270 & + [ 1pt ] & @xmath100 & @xmath24 & @xmath81 & @xmath271 & @xmath252  @xmath272  @xmath273 & @xmath255  @xmath274  @xmath275 & @xmath276 & @xmath186 & qso + [ 1pt ] & @xmath100 & @xmath54 & @xmath277 & @xmath278 & @xmath252  @xmath272  @xmath279 & @xmath255  @xmath274  @xmath280 & @xmath281 & @xmath242 & qso + [ 1pt ] & @xmath100 & @xmath60 & @xmath282 & @xmath283 & @xmath252  @xmath272  @xmath284 & @xmath255  @xmath274  @xmath285 & @xmath286 & @xmath119 & qso + [ 1pt ] & @xmath187 & @xmath24 & @xmath287 & @xmath288 & @xmath252  @xmath272  @xmath289 & @xmath255  @xmath274  @xmath290 & @xmath291 & @xmath204 & + [ 1pt ] & @xmath187 & @xmath54 & @xmath292 & @xmath293 & @xmath252  @xmath272  @xmath294 & @xmath255  @xmath274  @xmath295 & @xmath296 & @xmath204 & + [ 1pt ] & @xmath187 & @xmath60 & @xmath297 & @xmath298 & @xmath252  @xmath272  @xmath299 & @xmath255  @xmath274  @xmath300 & @xmath301 & @xmath66 & + [ 1pt ] & @xmath302 & @xmath24 & @xmath303 & @xmath304 & @xmath252  @xmath272  @xmath305 & @xmath255  @xmath274  @xmath218 & @xmath306 & @xmath307 & + [ 1pt ] & @xmath308 & @xmath24 & @xmath309 & @xmath310 & @xmath252  @xmath272 @xmath311 & @xmath255  @xmath312  @xmath313 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath24 & @xmath314 & @xmath315 & @xmath252  @xmath272 @xmath316 & @xmath255  @xmath312  @xmath317 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath24 & @xmath318 & @xmath319 & @xmath252  @xmath272 @xmath320 & @xmath255  @xmath312  @xmath321 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath54 & @xmath322 & @xmath323 & @xmath252  @xmath272 @xmath324 & @xmath255  @xmath312  @xmath325 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath54 & @xmath326 & @xmath327 & @xmath252  @xmath272 @xmath328 & @xmath255  @xmath312  @xmath329 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath54 & @xmath330 & @xmath331 & @xmath252  @xmath272 @xmath332 & @xmath255  @xmath312  @xmath333 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath54 & @xmath334 & @xmath335 & @xmath252  @xmath272 @xmath336 & @xmath255  @xmath312  @xmath337 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath54 & @xmath338 & @xmath339 & @xmath252  @xmath272 @xmath340 & @xmath255  @xmath312  @xmath341 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath60 & @xmath342 & @xmath343 & @xmath252  @xmath272  @xmath344 & @xmath255  @xmath312  @xmath345 &  &  & see appendix a + [ 1pt ] & @xmath308 & @xmath60 & @xmath61 & @xmath346 & @xmath252  @xmath272  @xmath347 & @xmath255  @xmath312  @xmath348 &  &  & see appendix a + ( 8.0,4.3 )    mid - infrared colours provide a powerful means of distinguishing between galaxies which contain agn and those that do not ( e.g. ivison et al . 2004 , 2007 ; egami et al . luminous galaxies at @xmath8 hosting agn have power - law mid - infrared spectra whereas those without agn are dominated by starlight in the irac bands and dust / pah emission at 24  @xmath2 m .    in fig . [ fig : colours ] we plot the ratio of 24 and 8  @xmath2 m flux density against the ratio of 8 and 4.5  @xmath2 m flux density for those objects detected in at least two _ spitzer _ bands . we superimpose redshift tracks for the local ulirgs mrk 231 ( agn - like sed ) and arp  220 and ngc  6240 ( starburst - like seds ) . the qsos and smgs clearly inhabit a different regions of this diagram . as expected the qsos have colours more similar to mrk  231 than to the starburst galaxies . three qsos have remarkably similar mid - infrared colours given that they were selected on their x - ray properties . the other qso , rx  j163308 , has significantly different irac colours but we note from the postage stamp image ( fig . [ fig : post1 ] ) that it has a close ` companion ' galaxy which is blended with the qso in our extracted catalogue and will thus contaminate the colours . while the other three qsos have @xmath349 m flux density ratios roughly consistent with the mrk  231 template at their known redshifts we note that their 24/8.0  @xmath2 m flux density ratios appear to be lower than that of mrk  231 by a factor of @xmath350 which might be related to the relative strength of emission / absorption features . all but one of the smgs on the other hand have mid - infrared colours consistent with arp 220 and/or ngc 6240 at @xmath8 . the one exception has colours consistent with arp  220 at @xmath351 but its faintness and non - detection at 24  @xmath2 m are more consistent with a mrk 231-like object at @xmath8 . it is thus the only smg in our sample for which mid - infrared colours indicate significant emission from an agn . we thus find no strong evidence for buried agn in the smgs . having said this , we note that deep x - ray ( e.g. vignati et al . 1999 ; netzer et al . 2005 ) and infrared spectroscopy ( e.g. lutz et al . 2003 ; armus et al . 2006 ) observations of ngc  6240 show that this galaxy does in fact host a highly obscured agn but that the energetics are dominated by the starburst . this leaves open the possibility that many of the smgs contain buried agn which are not powerful enough to dominate over the starburst in the mid - infrared . we have shown that the number counts of smgs with flux densities @xmath6  mjy in the @xmath352  arcmin diameter fields surrounding our x - ray absorbed qsos is higher than that found for a blank field . most of these galaxies have mid - infrared colours very similar to the local ulirg arp  220 if it were placed at @xmath8 . fitting the millimetre to far - infrared spectrum of arp  220 with a greybody and then integrating to determine the far - infrared luminosity we find l@xmath353  l@xmath14 which corresponds to a star - formation rate ( sfr ) of @xmath354  m@xmath14  yr@xmath21 after applying the usual scaling - law ( kennicutt 1998 ) . using the same greybody fit and applying the appropriate k - correction leads to predicted 850  @xmath2 m flux densities of 1.73 , 1.44 and 1.42 mjy for arp  220 at z=1 , 2 and 3 respectively . the smgs in our sample have 850  @xmath2 m flux densities ranging from about @xmath355 mjy implying that their sfrs range between @xmath356  m@xmath14  yr@xmath21 if arp  220 is indeed a good analogue . therefore , if the starburst can be sustained for a few hundred million years or so then a stellar mass equivalent to that of the bulge of a large galaxy will be assembled . it is natural to speculate that an over - dense region of space at high redshift containing galaxies that are capable of building large , homogeneous populations of stars will evolve over cosmic time to become clusters of galaxies containing a population of massive elliptical galaxies . since it is well established that elliptical galaxies contain dormant smbhs ( e.g. magorrian et al . 1998 ) , and that these must have assembled at high redshifts where the accretion luminosity density peaks , we expect that our smgs should contain growing black holes , i.e. agn . how the major growth phase of the black hole coincides temporally with the luminous starburst that builds up the stellar mass is a current topic of debate . indeed , models predict a range of possibilities ( e.g. archibald et al 2002 ; di matteo , springel & hernquist 2005 ) but there must be a link between the formation of the stars in the bulge and the smbh because of the tight correlation between their masses found for local galaxies ( ferrarese & merritt 2000 ) . after a number of early null results using moderate depth x - ray data ( e.g. fabian et al . 2000 ; waskett et al . 2003 ) deep x - ray ( alexander et al . 2005a , b , 2008 ) and mid - infrared spectroscopy ( menndez - delmestre et al . 2007 ; pope et al . 2008 ) observations show that smgs found in the field often do contain agn but that the masses of their black holes may be much smaller than those found in high redshift qsos , and consequently that the bulk of the far - infrared emission is due to the starburst . moreover , estimates of the host galaxy masses suggest that the growth of the black hole lags the growth of the spheroid ( borys et al . 2005 ; alexander et al . 2008 ; see also coppin et al . 2009 ) . while this may be the case for smgs , analysis of massive galaxies selected on other criteria find evidence to the contrary , suggesting that more than one scenario is possible for the formation of a massive galaxy and its smbh . for example , studies of powerful radio sources ( mclure et al . 2006 ) and luminous qsos ( peng et al . 2006 ) suggest that the black - hole mass to bulge luminosity ratio increases towards high redshifts thus indicating that the black hole reaches its critical mass before the galaxy bulge is fully formed . the mid - infrared colours of our smgs also argue against the presence of a powerful agn in these objects unless they are very highly obscured . they are thus either intrinsically different objects to the qso or they are caught at a different time in their evolution . page et al . ( 2010 , in prep . ) argue that the x - ray absorption in the qsos has its origin in an ionized absorber associated with a powerful wind capable of terminating the star formation . such feedback is a popular ingredient of models since it leads naturally to the relationship between smbh mass and spheroid mass discussed above ( e.g. fabian 1999 ) . if the smgs in the same field evolve to form a cluster of ellipticals then they would presumably go through a similar evolutionary sequence to the qso but are caught at an earlier stage of their life cycle at @xmath8 . estimates of the stellar masses would be useful to put further constraints on their evolutionary status . to this end we are currently fitting models to optical through infrared data to determine photometric redshifts and restframe @xmath357-band luminosities ; an analysis of the rxj  094144 field is currently in progress ( carrera et al . 2010 , in prep . ) . one difference worthy of note between the findings of this paper and those for high - redshift ( typically @xmath358 ) radio galaxies ( hzrgs ) concerns very bright smgs in their fields . two of the seven hzrg fields imaged with scuba contain smgs with @xmath359 mjy ( stevens et al . 2003 ) whereas the brightest object found around the qsos has @xmath360  mjy . although the samples are too small to give a statistically significant result it appears that the smgs detected around the lower redshift , less powerful , radio - quiet agn have lower @xmath361 . a direct comparison is not informative because the sources were extracted with different signal - to - noise criteria and by different methods but comparing flux densities significantly above the catalogue cut - offs yields @xmath342 smgs with @xmath362  mjy in the 7 hzrg fields while only @xmath363 are detected around the 5 qsos . given the effectively flat relationship between @xmath361 and redshift for @xmath364 this difference in flux density leads to a proportional difference in star - formation rates ( all other things being equal ) . there is thus reasonably good evidence for a difference in star - formation activity in individual galaxies in these fields indicating that the galaxy formation process might be dependent on the magnitude of the density peak and/or its redshift . for example , in the case of hzrgs it was found that the detection rate increased dramatically at @xmath365 ( archibald et al . 2001 ; reuland et al . 2004 ) which is significantly higher than the average redshift of our qso sample . another possibility is that the radio properties of the central agn are in some way linked to environmental density ( e.g. kauffmann , heckman & best 2008 ) . indeed , recent work by falder et al . ( 2010 ) finds evidence for larger over - densities of galaxies around radio - loud objects ( based on work carried out at 3.6  @xmath2 m ) . perhaps radio synchrotron luminosity is enhanced in regions where the inter - galactic medium is more dense . an obvious next step will be to conduct a statistically meaningful survey of fields around agn over the full range of redshifts in order to track star - formation activity as a function of cosmic time . the next generation bolometer camera on the jcmt ( scuba-2 ) and spire / pacs on - board the _ herschel space observatory _ are instruments with good enough sensitivity to make such a campaign practical . it would also allow a bigger area to be mapped around each agn , better matching the size of proto - cluster regions predicted by numerical simulations . we thank ian smail for extensive comments on the draft manuscript and mark thompson for useful discussions . the james clerk maxwell telescope is operated by the joint astronomy centre on behalf of the science and technology facilities council of the united kingdom , the netherlands organisation for scientific research , and the national research council of canada . jcmt data were taken under project ids m03au46 , m03bu32 and m04bu14 . this work is based [ in part ] on observations made with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology under a contract with nasa . support for this work was provided by nasa through an award issued by jpl / caltech . , m.j.p . and f.j.c . acknowledge support from the royal society . f.j.c . acknowledges further support from the spanish ministerio de educacin y ciencia under project esp2006 - 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infrared counterparts to the smgs with those identified previously at optical and near - infrared wavelengths . we also discuss cases where likely mid - infrared counterparts were not catalogued because they fell just outside our formal search radii , and one case where an obvious smg was not found by our extraction algorithm ; these sources were not included in the analysis described in the main part of this paper . the scuba data for this field were published previously by stevens et al . ( 2004 ) . in the present paper we have treated the data slightly differently in the final reduction stages ( rebinning and smoothing ) . we also apply a formal source extraction algorithm in this work resulting in only 2 sources at 850  @xmath2 m and 4 at 450  @xmath2 m whereas stevens et al . ( 2004 ) simply identified peaks on the maps above a 3-@xmath367 signal - to - noise threshold , identifying 6 sources . as already noted in section  [ section : se ] the source extraction algorithm fails to detect sources that are blended which has undoubtedly affected the 850  @xmath2 m extraction . at 450  @xmath2 m we can see that sources 450#1 and 450#3 appear more elongated than the other two objects hinting that they may be resolved . it was these objects that stevens et al . ( 2004 ) identified as blends . inspection of the postage stamps shows that source * 850#2/450#2 * is coincident with a bright mid - infrared source detected in all 3 _ spitzer _ channels . this object was one of a pair of sources detected in the @xmath368- and @xmath357-bands by stevens et al . spitzer _ data show that the correct identification is the object with the redder @xmath369 colour since this object becomes progressively more prominent with increasing wavelength compared to its neighbour and is detected at 24  @xmath2 m . source * 450#3 * falls in a crowded field . we find 2 possible identifications in the irac channels . of these source 206/160 lies closer to the 450  @xmath2 m source centroid and is also coincident with faint ( formally undetected ) emission at 24  @xmath2 m . source 206/160 was not one of the possible identifications discussed by stevens et al . ( 2004 ) since it is very faint / undetected in the @xmath357-band . we conclude that the likely identification for this smg is the very red object 206/160 . source * 450#4 * was matched with an extremely red object ( @xmath370 ) by stevens et al . this source is not formally recovered in this work because it lies outside our 5 arcsec irac search radius but is visible in the postage stamp to the west of the 450  @xmath2 m centroid as a bright source at 4.5 and 8.0  @xmath2 m . given its red colours we consider this object as a likely identification . measured flux densities are @xmath371 and @xmath372 @xmath2jy at 4.5 and 8.0  @xmath2 m respectively giving a colour similar to arp  220 at the redshift of the qso . the 4.5-@xmath2 m centroid is 6.6 arcsec from the extracted 450  @xmath2 m position at @xmath373 , @xmath374 while the 8.0-@xmath2 m centroid is 6.4 arcsec from the extracted 450  @xmath2 m position at @xmath375 , @xmath376 . the calculated p - statistic is 0.089 and 0.064 at 4.5 and 8.0  @xmath2 m respectively .      in section  [ section : catmem ] we noted that the qso in this field was not found by our extraction algorithm but was detected by page et al . the latter observations used scuba in ` photometry ' mode where the central bolometer of each array is centred on the target but no image is made . inspection of fig . [ fig : allmaps ] shows that while there is submillimetre emission at the location of the qso ( located below source 5 on the 850  @xmath2 m image ) the surrounding structure is complex . it is thus possible that the source extraction algorithm failed to locate a significant peak because of blending . it is also likely that the photometry observation of this object reported by page et al . ( 2001 ) is contaminated by emission from the smgs close to the qso .    in table [ table : spit ] we noted that object * 850#5 * has a likely false identification at 24  @xmath2 m . this can also be attributed to the crowded field close to the qso since it is the qso itself that has fallen within the search radius at 24  @xmath2 m while it was not picked up in the smaller search radii adopted for the irac channels . source * 850#2 * has no listed identification in table  [ table : spit ] but the postage stamp images show bright 4.5 and 8.0  @xmath2 m sources close to the 850  @xmath2 m centroid . the closest 4.5  @xmath2 m source is at @xmath378 , @xmath379 which at 5.3 arcsec from the smg is only just outside our formal search radius . this object has a flux density of @xmath380  @xmath2jy and is coincident with an 8.0  @xmath2 m source although the latter is not detected by sextractor . inspection of the 8.0  @xmath2 m image reveals that the diffraction spike from the bright qso at the field centre falls on top of this object probably explaining the non - detection . although the p - statistic for the 4.5  @xmath2 m source is high at 0.259 we consider this object as a likely identification because of its detection in both irac bands . source * 850#4 * has no listed identification in table  [ table : spit ] but the postage stamp images show a bright 4.5 and 8.0  @xmath2 m source close to the 850  @xmath2 m centroid along with faint ( formally undetected ) emission at 24  @xmath2 m . the 4.5  @xmath2 m source is located at @xmath381 , @xmath382 only 5.2 arcsec from the smg , has a flux density of @xmath383 and a p - statistic of 0.266 . the 8.0  @xmath2 m source is located at @xmath384 , @xmath385 only 5.9 arcsec from the smg , has a flux density of @xmath386 and a p - statistic of 0.198 . this object has irac colours similar to arp  220 at the redshift of the qso . the proximity of this object to the smg together with its detection in in both irac bands make it a likely identification . inspection of the 850  @xmath2 m map for this field ( fig . [ fig : allmaps ] ) shows submillimetre emission north of the qso at approximately @xmath387 , @xmath388 . there is a negative region to the east of this position which is consistent with a negative image of the source located at one of the off - positions . the western off - position would fall off the map . we believe that this is a real smg ( probably two sources ) which was missed by the extraction algorithm because of its proximity to the edge of the map . inspection of the postage stamp images reinforces this belief since we find two 24  @xmath2 m sources coincident with the smg position and at the same approximate position angle as the 850  @xmath2 m emission . the irac data reveal 3 and 5 sources at 4.5 and 8.0  @xmath2 m respectively . the southern 24/850  @xmath2 m source has two possible irac identifications . of these , source 260/232 is the brightest and reddest object ; its @xmath349 m flux density ratio is @xmath389 . if source 10 is the 24  @xmath2 m counterpart then the ratio of flux densities at 24 and 8.0  @xmath2 m is @xmath390 which would place this object on the mrk  231 curve shown in fig  [ fig : colours ] indicating that it hosts a buried agn , possibly at a lower redshift than rx  j163308 . the northern 24/850  @xmath2 m source has 1 counterpart at 4.5  @xmath2 m and 3 at 8.0  @xmath2 m although the 4.5  @xmath2 m emission is extended in the same manner as that at 8.0  @xmath2 m implying that this smg could have multiple mid - infrared counterparts . inspection of the flux densities presented in table  [ table : spit ] shows that the irac colours are similar to those of arp  220 at the redshift of the qso so this source is unlikely to host an agn . since this system is one of the most interesting in our sample we include it in table  [ table : spit ] as source * 850#7 * although it is not included in the 850  @xmath2 m number counts analysis because it was not found by the extraction algorithm .
we present submillimetre and mid - infrared imaging observations of five fields centred on quasi - stellar objects ( qsos ) at @xmath0 . 
 all @xmath1 qsos were detected previously at submillimetre wavelengths . at 850 ( 450 ) 
 @xmath2 m we detect 17 ( 11 ) submillimetre galaxies ( smgs ) in addition to the qsos . 
 the total area mapped at 850  @xmath2 m is @xmath3  arcmin@xmath4 down to rms noise levels of @xmath5 mjy / beam , depending on the field . 
 integral number counts are computed from the 850  @xmath2 m data using the same analytical techniques adopted by ` blank - field ' submillimetre surveys . 
 we find that the ` qso - field ' counts show a clear excess over the blank - field counts at deboosted flux densities of @xmath6 mjy ; at higher flux densities the counts are consistent with the blank - field counts . 
 robust mid - infrared counterparts are identified for all four submillimetre detected qsos and @xmath7 per cent of the smgs . 
 the mid - infrared colours of the qsos are similar to those of the local ulirg / agn mrk  231 if placed at @xmath8 whilst most of the smgs have colours very similar to those of the local ulirg arp  220 at @xmath8 . 
 mid - infrared diagnostics therefore find no strong evidence that the smgs host buried agn although we can not rule out such a possibility . 
 taken together our results suggest that the qsos sit in regions of the early universe which are undergoing an enhanced level of major star - formation activity , and should evolve to become similarly dense regions containing massive galaxies at the present epoch . 
 finally , we find evidence that the level of star - formation activity in individual galaxies appears to be lower around the qsos than it is around more powerful radio - loud agn at higher redshifts . 
 galaxies : formation - galaxies : starburst - galaxies : evolution - galaxies : high redshift - submillimetre - qso : general