  We consider some aspects of counting BPS operators which are annihilated by
two supercharges, in superconformal field theories. For non-zero coupling, the
corresponding multi-variable partition functions can be written in terms of
generating functions for vector partitions or their weighted generalisations.
We derive asymptotics for the density of states for a wide class of such
multi-variable partition functions. We also point out a particular
factorisation property of the finite N partition functions. Finally, we discuss
the concept of a limit curve arising from the large N partition functions,
which is related to the notion of a typical state and discuss some implications
for the holographic duals.
