Tectonic plates are formed and move apart at mid-ocean ridges. Some portion of this plate-separation process can occur by stretching of the crust, resulting in a complex pattern of extensional faults. Abyssal hills, the most ubiquitous topographic features on Earth, are thought to be a product of this faulting,. Here we report the results of a self-consistent numerical model of lithospheric formation and stretching that includes spontaneous fault creation. In this model, an axial valley develops where the fault activity is most concentrated. The `frozen' fault-generated topography, rafted out of the axial valley, is visually and statistically similar to observed abyssal hills formed at many slower-spreading ridges. Faults appear to be replaced by new faults because their offset changes the local stress field. We accordingly need no temporal variation in magmatism, as required by some previous models, to control the spacing or offset of faults. Our model results suggest instead that the irregularity of abyssal hill relief may result from a self-organized critical stress state at spreading centres.