  We study random composite structures considered up to symmetry that are
sampled according to weights on the inner and outer structures. This model may
be viewed as an unlabelled version of Gibbs partitions and encompasses
multisets of weighted combinatorial objects. We describe a general setting
characterized by the formation of a giant component. The collection of small
fragments is shown toconverge in total variation toward a limit object
following a P\'olya-Boltzmann distribution.
