A simple two-dimensional model has been used to examine the influence of growth-rate anisotropy, nucleation (seeding) density, and orientation of nuclei on the crystallization kinetics and extent of crystal orientation in thin films. It has been shown that variations in growth-rate anisotropy produce large changes in the kinetics, but relatively small changes in crystal orientation. On the other hand, the orientation of the nuclei has a small influence on the kinetics of crystallization, but strongly influences the extent of crystal orientation at early times.