Growth models for discontinuous films

We study some variants of the Smoluchowski coagulation equation as applied to different regimes of submonolayer film growth. Scaling properties and growth exponents are studied. The equation represents a mean field description. The first part of the paper reviews our current understanding of the range of validity of this description as applied to diffusion dominated growth processes and, in particular, identifies at what point it is necessary to go beyond mean field theory. The second part of the paper presents some new results from a mean field approach applied to a coalescence dominated growth model.