  We find limit shapes for a family of multiplicative measures on the set of
partitions, induced by exponential generating functions with expansive
parameters, $a_k\sim Ck^{p-1}, k\to\infty, p>0$,where $C$ is a positive
constant. The measures considered are associated with reversible
coagulation-fragmentation processes and certain combinatorial structures, known
as assemblies. We prove the functional central limit theorem for the
fluctuations of a scaled random partition from its limit shape. We demonstrate
that when the component size passes beyond the threshold value, the
independence of numbers of components transforms into their conditional
independence. Among other things, the paper also discusses, in a general
setting, the interplay between limit shapes, threshold and gelation.
