Landscapes of the U.S. Central Lowland were repeatedly affected by the Laurentide Ice Sheet. Glacial processes diminished relief and disrupted drainage networks. Deep valleys carved by meltwater were disconnected from the surrounding uplands. The upland area lacking surface water connection to the drainage network is referred to as noncontributing area (NCA). Decreasing fractions of NCA on older surfaces suggest that NCA becomes drained over time. We propose that the integration could occur via (1) capture of NCA as channels propagate into the upland or (2) subsurface or intermittent surface connection of NCA to external drainage networks providing increased discharge to promote channel incision. We refer the two cases as “disconnected” and “connected” since the crucial difference between them is the hydrological connection of the upland to external drainage. We investigate the differences in evolution and morphology of channel networks in low‐relief landscapes under disconnected and connected regimes using numerical simulations. We observe substantially faster rates of erosion and integration of the channel network in the connected case. The connected case also creates longer, more sinuous channels than the disconnected case. Sensitivity tests indicate that hillslope diffusivity has little influence on the evolution and morphology. The fluvial erosion coefficient has significant impact on the rate of evolution, and it influences the morphology to a lesser extent. Our results and a qualitative comparison with landscapes of the glaciated U.S. Central Lowland suggest that connection of NCAs is a potential control on the evolution and morphology of postglacial landscapes.