  We consider two sequential models of deposition and aggregation for
particles. The first model (No Diffusion) simulates surface diffusion through a
deterministic capture area, while the second (Sequential Diffusion) allows the
atoms to diffuse up to \ell steps. Therefore the second model incorporates more
fluctuations than the first, but still less than usual (Full Diffusion) models
of deposition and diffusion on a crystal surface. We study the time dependence
of the average densities of atoms and islands and the island size distribution.
The Sequential Diffusion model displays a nontrivial steady-state regime where
the island density increases and the island size distribution obeys scaling,
much in the same way as the standard Full Diffusion model for epitaxial growth.
Our results also allow to gain insight into the role of different types of
fluctuations.
