Rill networks have been a focus of study for many decades, but we still lack a complete understanding of the variables that control the spacing of rills and the geometry of rill networks (e.g., parallel or dendritic) on hillslopes. In this paper, we investigate the controls on the spacing and geometry of rill networks using numerical modeling and comparison of the model results to terrestrial-laser-scanner-derived topographic data from rill networks formed in physical experiments. The landscape evolution model accounts for the transport of sediment due to rain splash and fluvial entrainment as well as the deposition of sediment being advected by the overland flow. In order to develop realistic rill networks in the model, we find that it is necessary to incorporate the effects of raindrop impact within the fluvial sediment transport process. Model results are only consistent with those of experiments when raindrop-aided fluvial sediment transport is accounted for. Dendritic networks are often predicted by the model in cases of high initial topographic roughness and high rates of advective (fluvial) sediment transport relative to diffusive (colluvial) transport. Parallel networks form within numerical experiments in low-roughness cases under a wide range of relative advective and diffusive transport rates as well as in high roughness cases in which diffusive sediment transport is high relative to advective transport. The transition from dendritic to parallel rill networks is shown to occur gradually rather than being associated with a particular threshold. Finally, based on a balance between diffusive and advective sediment transport processes, we predict that the mean spacing between parallel rills scales with the square root of the ratio of diffusivity to channel erodibility.