In a new model proposed for the formation of submarine canyons and submarine fan-aprons, numerical simulations of basin fill are utilized to illustrate simple concepts of slope grading. This modeling suggests that erosional truncation, sediment bypass, and marine onlap of submarine fan-apron complexes are formed in response to changing basin physiography. Two kinds of basin margins are identified. (1) Progradational margins represent the basinward advance of graded depositional profiles formed when diffusive and sediment gravity-flow processes are in equilibrium with sediment supply, basin subsidence, and basin physiography. (2) Erosional margins form when upper slope gradients exceed an equilibrium grade, and are characterized by erosion, slumping, and sediment bypass to lower slope environments via sediment gravity-flow processes. Erosional margins are transformed into progradational margins when the bathymetric escarpment (i.e., an oversteepened margin) is buried by onlapping and aggrading fanapron deposits. Progradational margins can develop bathymetric escarpments and become erosional in response to a rapid rise in relative sea level, structural deformation of basin profiles (e.g., faulting), and/or a transition from carbonate to siliciclastic deposition. Whereas relative falls in sea level play a major role in bringing the source of sediment input to the shelf edge, the development of slope unconformities and onlapping submarine fan-apron systems is controlled primarily by slope- readjustment processes triggered by changing basin physiography.