Experimental results presented here quantify how the thickness of turbidity currents affects the evolution of an aggrading subaqueous channel. Ten sediment-laden currents with identical initial conditions were released into a tank to determine how depositional flows interact with and modify a pre-existing channel form. Deposition was always greatest on the channel floor, systematically reducing channel depth and causing the ratio of initial current thickness to channel depth to increase with each flow. The ratio of longitudinal to lateral current velocity decreased exponentially with increasing relative current thickness. This change in lateral spreading demarcated regimes of channelized, quasi-channelized, and unconfined flow. Channelized currents have thicknesses that are less than 1.3 times local channel depth; unconfined currents are greater than five times channel depth; and quasi-channelized currents occur in between. The unconfined cases were consistent with prior experiments and theory defining the flow field for nonchannelized turbidity currents. Sedimentation patterns for even the thickest currents were influenced by subdued channel topography.