  We consider a model of aggregation, both diffusion-limited and ballistic,
based on the Cayley tree. Growth is from the leaves of the tree towards the
root, leading to non-trivial screening and branch competition effects. The
model exhibits a phase transition between ballistic and diffusion-controlled
growth, with non-trivial corrections to cluster size at the critical point.
Even in the ballistic regime, cluster scaling is controlled by extremal
statistics due to the branching structure of the Cayley tree; it is the
extremal nature of the fluctuations that enables us to solve the model.
