  We explore the crystallization in a colloidal monolayer on a structured
template starting from a few-particle nucleus. The competition between the
substrate structure and that of the growing crystal induces a new crystal
growth scenario. Unlike with the crystal growth in the bulk where a
well-defined and connected crystal-fluid interface grows into the fluid, we
identify a mechanism where a "compatibility wave" of the prescribed nucleus
with the underlying substrate structure dictates the growth direction and
efficiency. The growth process is strongly anisotropic and proceeds via
transient island formation in front of an initial solid-fluid interface. We
demonstrate the validity of this compatibility wave concept for a large class
of substrate structures including a square-lattice and a quasicrystalline
pattern. Dynamical density functional theory which provides a microscopic
approach to the crystallization process is employed for colloidal hard spheres.
Our predictions can be verified in experiments on confined colloids and also
bear consequences for molecular crystal growth on structured substrates.
