Submonolayer epitaxy is studied with two simple theoretical models whe
re adatom exchange with a surface atom yields a stable nucleus for isl
and growth. The results are relevant to systems where surface layer in
clusions are formed by alloying and where buried islands are formed in
the presence of surfactants. Rate equations and Monte Carlo simulatio
ns are used to study the evolution of the island size distributions. T
he rate equations reproduce all of the qualitative features found in b
oth the simulations and in recent experiments when the coverage-depend
ent rate of adatom capture by islands is calculated self-consistently.