tokens: groups: good ( LR > 0.25), fair (0.05 LR 0.25), and bad ( LR 0.25). In addition, as a cross-check we calculated the simple probability of chance coincidence, according to Downes et al. (1986) . We then assigned a preliminary rank, rejecting most of the cases with bad scores. A primary single counterpart is either a physical solitary association, a single non-bad association, or exceptionally the best of the rejects that has been “recovered”. When several candidates above the threshold exist, the one with the best estimator is considered the primary counterpart, and all the others secondaries. The detailed procedure can be found in XXL Paper XXVII. 2.4 Optical photometry The BCS covers ~50 deg 2 , fully covering XXL-S. Optical data in the griz bands were obtained with the Mosaic2 imager mounted on the Cerro Tololo Inter-American Observatory (CTIO) 4m Blanco telescope, reaching 10 σ point source depths of 23.9, 24.0, 23.6, and 22.1 mag (AB) in the four bands (for more details see Desai et al. 2012 ). The DECam ( Flaugher et al. 2015 ) mounted on the Blanco telescope also observed XXL-S (PI: C. Lidman) in the griz bands (4850−9000 Å). The limiting magnitudes in each band (defined as the third quartile of the corresponding magnitude distribution) reach 25.73, 25.78, 25.6, and 24.87 mag (AB). More details of the observations can be found in XXL Paper VI and in Desai et al. (2012 , 2015 ). 2.5 Optical spectroscopy A significant effort has been made to obtain spectroscopy of both northern and southern XXL fields, either with large spectroscopic surveys, for example SDSS, VIPERS ( Scodeggio et al. 2018 ), GAMA ( Baldry et al. 2018 ), ESO Large Program ( Adami et al. 2018 , a.k.a. XXL Paper XX), or smaller scale spectroscopic observations, like the William Herschel Telescope (WHT) spectroscopic follow-up program ( Koulouridis et al. 2016 , XXL Paper XII). The southern field has been chosen for this study due to the homogeneity of its spectroscopic follow-up data, which is based uniquely on a number of observing runs with the multifibre 2dF+AAOmega facility on the AAT; instead, the northern field is based on a compilation of different surveys with different instruments, limiting magnitudes, selection biases, and solid angles.The first set of AAOmega runs occurred in 2013, and is described in Lidman et al. (2016 , hereafter XXL Paper XIV). The second set of runs occurred in 2016 and is described in XXL Paper XXVII. As noted in XXL Paper XIV, priority was given to cluster galaxies over AGN in the 2013 observations. In the 2016 set of observations, AGNs had the highest priority. Hence, the coverage of the AGNs is, perhaps apart from the smallest scales, uniform. It should also be remembered that there is always a lower fibre separation limit, which for the AAOmega case is , corresponding to ~0.2 h −1 Mpc at the median redshift of our sample. However, since any given region within the XXL area was targeted multiple times with 2dF, the number of objects lost
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