The formation of nuclei of a new phase and their growth on the inhomogeneou
s substrate from a vapor phase are studied. Basic kinetic equations describ
ing such a process are solved numerically. The effect of the depletion of a
ctive sites during the growth of nuclei is taken into account. Basic charac
teristics of the nucleation process, such as size distribution function, nu
cleation rate and number of nuclei formed on the unit surface are determine
d. It is shown that the size distribution of nuclei evolves by a nontrivial
way as a function of time. This process is fully nonstationary from the vi
ewpoint of nucleation rate. The total number of nuclei reaches the number o
f active centers for a sufficiently long time.