The unboundedness locus L(u) of a plurisubharmonic function u is the set of points x∈X such that u is unbounded in every neighbourhood of x. It always contains the polar locus of u. One knows that the polar locus of a non-trivial psh function is of zero Lebesgue-measure for instance, but is there anything similar known about L(u)? 



How large is the unboundedness locus of a plurisubharmonic function?
$L(u)$ can be the whole domain. In dimension $1$, take a dense countable
set $\{ z\_k\}$ and consider the 
(pluri) subharmonic function $\sum\_k a\_k\log|z-z\_k|$, where $a\_k>0$ tend to zero sufficiently fast. In other words, a (pluri) polar set where the (pluri)
subharmonic function equals $-\infty$ can be dense.


