  This paper concerns the long term behaviour of a growth model describing a
random sequential deposition of particles on a finite graph. The probability of
allocating a particle at a vertex is proportional to a log-linear function of
numbers of existing particles in a neighbourhood of a vertex. When this
function depends only on the number of particles in the vertex, the model
becomes a special case of the generalised Polya urn model. In this special case
all but finitely many particles are allocated at a single random vertex almost
surely. In our model interaction leads to the fact that, with probability one,
all but finitely many particles are allocated at vertices of a clique.
