  We study a hierarchical model of non-overlapping cubes of sidelengths $2^j$,
$j \in \mathbb{Z}$. The model allows for cubes of arbitrarily small size and
the activities need not be translationally invariant. It can also be recast as
a spin system on a tree with long-range hard-core interaction. We prove
necessary and sufficient conditions for the existence and uniqueness of Gibbs
measures, discuss fragmentation and condensation, and prove bounds on the decay
of two-point correlation functions.
