  This study extends a prior investigation of limit shapes for partitions of
integers, which was based on analysis of sums of geometric random variables.
Here we compute limit shapes for grand canonical Gibbs ensembles of partitions
of sets, which lead to the sums of Poisson random variables. Under mild
monotonicity assumptions, we study all possible scenarios arising from
different asymptotic behaviors of the energy, and also compute local limit
shape profiles for cases in which the limit shape is a step function.
