  In this paper we consider the dynamics of point islands during submonolayer
deposition, in which the fragmentation of subcritical size islands is allowed.
To understand asymptotics of solutions, we use methods of centre manifold
theory, and for globalisation, we employ results from the theories of
compartmental systems and of asymptotically autonomous dynamical systems. We
also compare our results with those obtained by making the quasi-steady state
assumption.
