  We study the evolution of an initially random distribution of particles on a
square lattice, under certain rules for `growing' and `culling' of particles.
In one version we allow the particles to move laterally along the surface
(mobile layer) and in the other version this motion is not allowed (immobile
case). In the former case both analytical and computer simulation results are
presented, while in the latter only simulation is possible. We introduce growth
and culling probabilities appropriate for condensation and evaporation on a
two-dimensional surface, and compare results with existing models for this
problem. Our results show very interesting behaviour, under certain conditions
quite different from earlier models. We find a possibility of hysteresis not
reported earlier for such models. ~
