  We investigate a model of interacting clusters which compete for growth. For
a finite assembly of coupled clusters, the largest one always wins, so that all
but this one die out in a finite time. This scenario of `survival of the
biggest' still holds in the mean-field limit, where the model exhibits glassy
dynamics, with two well separated time scales, corresponding to individual and
collective behaviour. The survival probability of a cluster eventually falls
off according to the universal law $(\ln t)^{-1/2}$. Beyond mean field, the
dynamics exhibits both aging and metastability, with a finite fraction of the
clusters surviving forever and forming a non-trivial spatial pattern.
