This article reflects on the growth of films where the orientation of the initial crystallites is guided by the substrate, viz., epitaxial growth. The growth dynamics under such conditions have been simulated for crystals taking the shapes of cubes and octahedra. The simulations are based on the growth dynamics for ideal atomic layer deposition (ALD) processes, but the outcome is also applicable to other processes under certain assumptions. The topography and growth statistics are evaluated as functions of different types of positioning and magnitudes of tilting of the crystallites relative to the substrate. Growth situations where additional seed crystallites are nucleated on the film surface during the growth are also simulated. A non-linear type of growth in the initial stages of the growth process is identified for all cases considered and, depending on the crystallites, orientations and their nucleation pattern, may be interpreted as type-1 or type-2 substrate-inhibited growth. A concept dividing epitaxial growth into stable and labile growth is advanced. Stable and labile epitaxial growth is ascribed to the situations where the fastest growth direction is normal and parallel to the substrate plane, respectively. The results indicate that epitaxial films of cubic materials with (100) and (1 1 1) orientation for cube- and octahedron-shaped crystals, respectively, are labile and therefore possibly undesirable orientations for growth of high quality films. (C) 2007 Elsevier B.V. All rights reserved.