Several aspects of self-ordering are predicted by Monte Carlo simulations for a model system in which crystallization of polymers on a pre-patterned surface is simulated. The pattern consists of parallel lanes which have alternately a high and low affinity with respect to particle adsorption. Prior to crystallization, an anisotropic melt density profile is established. A nucleus located perpendicular to the lanes acts as a seed where crystallization starts. Initially, the anisotropic melt density profile causes each high affinity lane to crystallize. As time proceeds less crystals will be able to continue to grow. Surviving crystals 1 grow at constant speed, 2 do not switch lanes, and 3 are nonrandomly distributed showing a characteristic intercrystal distance, which is represented by a strongly peaked structure function in the direction perpendicular to the lanes. Besides the self-ordering, we also find that the crystal growth velocity on the patterned substrate is higher than for a nonpatterned substrate. We propose underlying mechanisms to be generally applicable for several growth models. © 2003 American Institute of Physics.