In previous work we have developed a computational framework for topographic map formation and plasticity based on axonal process sprouting and retraction, in which sprouting and retraction are governed by competition for neurotrophic support. Here we show that such an approach can account for certain aspects of the dendritic morphology of cortical maps. In particular, we model the development of ocular dominance columns in the primary visual cortex and show that cortical cells near to column boundaries prefer to elaborate dendritic fields which avoid crossing the boundaries. This emerges as different functional inputs are spatially separated. We predict that afferent segregation occurs before or simultaneously with, but not after, the emergence of dendritic bias. We predict that animals reared with complete but asynchronous stimulation of the optic nerves do not develop a dendritic bias. We suggest that the emergence of a dendritic bias might provide a partial account for the critical period for a response to monocular deprivation. In particular, we predict that animals reared with asynchronous optic nerve stimulation might exhibit an extended critical period. Our results also indicate that the number of synapses supported by cortical cells depends on the intra–ocular image correlations used in our simulations. This suggests that inter–ocular image correlations, and thus strabismic rearing of kittens, may also affect the innervation density.