  For $\widetilde{\cal R} = 1 - \exp(- {\cal R})$ a random closed set obtained
by exponential transformation of the closed range ${\cal R}$ of a subordinator,
a regenerative composition of generic positive integer $n$ is defined by
recording the sizes of clusters of $n$ uniform random points as they are
separated by the points of $\widetilde{\cal R}$. We focus on the number of
parts $K_n$ of the composition when $\widetilde{\cal R}$ is derived from a
gamma subordinator. We prove logarithmic asymptotics of the moments and central
limit theorems for $K_n$ and other functionals of the composition such as the
number of singletons, doubletons, etc. This study complements our previous work
on asymptotics of these functionals when the tail of the L\'evy measure is
regularly varying at $0+$.
