Continental rifting is responsible for the generation of major sedimentary basins, both during rift inception and during the formation of rifted continental margins. Geophysical and field studies revealed that rifts feature complex networks of normal faults but the factors controlling fault network properties and their evolution are still matter of debate. Here, we employ high-resolution 2D geodynamic models (ASPECT) including two-way coupling to a surface processes code (FastScape) to conduct 12 models of major rift types that are exposed to various degrees of erosion and sedimentation. We further present a novel quantitative fault analysis toolbox (Fatbox), which allows us to isolate fault growth patterns, the number of faults, and their length and displacement throughout rift history. Our analysis reveals that rift fault networks may evolve through five major phases: 1) distributed deformation and coalescence, 2) fault system growth, 3) fault system decline and basinward localization, 4) rift migration, and 5) breakup. These phases can be correlated to distinct rifted margin domains. Models of asymmetric rifting suggest rift migration is facilitated through both ductile and brittle deformation within a weak exhumation channel that rotates subhorizontally and remains active at low angles. In sedimentation-starved settings, this channel satisfies the conditions for serpentinization. We find that surface processes are not only able to enhance strain localization and to increase fault longevity but that they also reduce the total length of the fault system, prolong rift phases and delay continental breakup.