Transient 3D substrate nucleation and growth from the vapor phase on the active sites is studied. The set of kinetic equations describing the formation of nuclei, including the depletion of active sites during nucleation, has been solved numerically within standard nucleation theory to obtain the time-dependent size distribution function of nuclei. Knowing the size distribution function. the basic characteristics of nucleation process (such as nucleation rate, the total number of nuclei formed on the active sites) are determined. It is shown that the evolution of the size distribution function up to the large cluster sizes (40 000 molecules in the cluster) is a complex process. At sufficiently long time, maximum on size distribution (typical for heterogeneous nucleation) appears. The integrated cluster flux (i.e., the number of nuclei greater than given cluster size) reaches for sufficiently long time its stationary value, which is equal to the number of active sites.