  We consider a system of clusters made of elementary building blocks,
monomers, and evolving via collisions between diffusing monomers and immobile
composite clusters. In our model, the cluster-monomer collision can lead to the
attachment of the monomer to the cluster (addition process) or to the total
break-up of the cluster (shattering process). A phase transition, separating
qualitatively different behaviors, occurs when the probability of shattering
events exceeds a certain threshold. The novel feature of the phase transition
is the dramatic dependence on the initial conditions.
