Classical growth models, such as that of Burton, Cabrera and Frank, assume step motion driven by the diffusion of atomic species with the steps acting as sinks. The presence of steps on both reconstructed and unreconstructed surfaces of substrates used for the growth of superconducting films, such as SrTiO3, and observations of nucleation along such steps, provide an opportunity to investigate the applicability of growth models, with suitable modifications for higher volume supersaturations encountered in processes such as molecular beam epitaxy. Diffraction information suggests the formation of an unstable phase as a precursor of the 123 phase. Although the kinetics of formation of the 123 phase remains unclear, the presence of the unstable phase suggests that kinetics may be governed by additivity of cation fluxes. Analysis yields a rate of advance of steps of the order of 1nm/s. Island size and misorientation distributions are presented for films of two different thickness. Reasonably good agreement of island sizes is obtained with experiment for ultrathin films of DyBa2Cu3O7-x with thickness of 40 and 100 Å.