  Point island models (PIMs) are presented for the formation of supported
nanoclusters (or islands) during deposition on flat crystalline substrates at
lower submonolayer coverages. These models treat islands as occupying a single
adsorption site, although carrying a label to track their size (i.e., they
suppress island structure). However, they are particularly effective in
describing the island size and spatial distributions. In fact, these PIMs
provide fundamental insight into the key features for homogeneous nucleation
and growth processes on surfaces. PIMs are also versatile being readily adapted
to treat both diffusion-limited and attachment-limited growth, and also a
variety of other nucleation processes with modified mechanisms. Their behavior
is readily and precisely assessed by kinetic Monte Carlo simulation.
