We study the evolution of two-dimensional nuclei and holes on the isot
ropic surface during both crystal growth and growth interruption. We s
how that there are fundamental differences between the nuclei evolutio
n in the absence of an outer source of condensing atoms, which is desc
ribed by the theory of Lifshitz and Slezov, and that in the presence o
f such a source, i.e. during epitaxial growth. We also consider the ev
olution of the nuclei size distribution function, which is also differ
ent for these two cases.