We investigate the origin of mid-ocean ridge morphology with numerical models that successfully predict axial topographic highs, axial valleys, and the transition between the two. The models are time-dependent, simulating alternating tectonic and magmatic periods where far-field extension is accommodated by faulting and by magmatism, respectively. During tectonic phases, models predict faults to grow on either side of the ridge axis and axial height to decrease. During magmatic phases, models simulate magmatic extension by allowing the axial lithosphere to open freely in response to extension. Results show that fault size and spacing decreases with increasing time fraction spent in the magmatic phase FM. Magmatic phases also simulate the growth of topography in response to local buoyancy forces. The fundamental variable that controls the transition between axial highs and valleys is the “rise-sink ratio,” (FM/FT)(τT/τM), where FM/FT is the ratio of the time spent in the magmatic and tectonic periods and τT/τM is the ratio of the characteristic rates for growing topography during magmatic phases (1/τM) and for reducing topography during tectonic phases (1/τT). Models predict the tallest axial highs when (FM/FT)(τT/τM) ≫ 1, faulted topography without a high or valley when (FM/FT)(τT/τM) ∼ 1, and the deepest median valleys when (FM/FT)(τM/τT) < 1. New scaling laws explain a global negative correlation between axial topography and lithosphere thickness as measured by the depths of axial magma lenses and microearthquakes. Exceptions to this trend reveal the importance of other behaviors such as a predicted inverse relation between axial topography and spreading rate as evident along the Lau Spreading Center. Still other factors related to the frequency and spatial pervasiveness of magmatic intrusions and eruptions, as evident at the Mid-Atlantic and Juan de Fuca ridges, influence the rise-sink-ratio (FM/FT)(τT/τM) and thus axial morphology.