Magma supply likely exerts primary control on seafloor morphology of oceanic crust, but most studies have related morphology to spreading rate. Here we examine global patterns of morphology on mid‐ocean ridge (MOR) flanks in relation to magma supply derived from residual mantle Bouguer gravity anomaly (proxy for relative crustal thickness) and spreading rate. We use multibeam bathymetry to characterize morphology using both qualitative (descriptive) and quantitative approaches, and we compare results to both magma supply and spreading rate. Morphology becomes more isotropic and abyssal hills are more irregular and discontinuous as magma supply decreases, while roughness, area of steeper slopes, and anomalous fabric orientation increase. We interpret these changes to reflect changing magma distribution along‐axis, from large‐volume and spatially extensive to progressively reduced, increasingly localized, and more irregularly emplaced. Observed relations between crustal thickness and morphology imply that average thickness of purely magmatic crust in the Atlantic and parts of the Indian ridge system is significantly less than average seismically determined crust. Thus seismically defined crustal thickness in those regions likely includes significant non‐magmatic components such as serpentinized mantle. Excepting regions of extensive mantle exposure, most morphologic parameters that we examined are sensitive to estimated magma supply but not necessarily to spreading rate alone. We summarize our results in schematic models that relate morphologic variations to changes in magma supply and mantle serpentinization throughout the global MOR system. Finally, we note that combined qualitative and quantitative results of our study may be useful for developing automated morphologic classification schemes.