While recent experimental work has defined asymmetries and lateralization in left and right cortical maps, the mechanisms underlying these phenomena are currently not established. In order to explore some possible mechanisms in theory, we studied a neural model consisting of paired cerebral hemispheric regions interacting via a simulated corpus callosum. Starting with random synaptic strengths, unsupervised (Hebbian) synaptic modifications led to the emergence of a topographic map in one or both hemispheric regions. Because of uncertainties concerning the nature of hemispheric interactions, both excitatory and inhibitory callosal influences were examined independently. A sharp transition in model behavior was observed depending on callosal strength. For excitatory or weakly inhibitory callosal interactions, complete and symmetric mirror-image maps generally appeared in both hemispheric regions. In contrast, with stronger inhibitory callosal interactions, partial to complete map lateralization tended to occur, and the maps in each hemispheric region often became complementary. Lateralization occurred readily toward the side having a larger cortical region or higher excitability. Asymmetric synaptic plasticity, however, had only a transitory effect on lateralization. These results support the hypotheses that interhemispheric competition occurs, that multiple underlying asymmetries may lead to function lateralization, and that the effects of asymmetric synaptic plasticity may vary depending on whether supervised or unsupervised learning is involved. To our knowledge, this is the first computational model to demonstrate the emergence of topographic map lateralization and asymmetries.