Deposition from particle-laden flows is often described in terms of the capacity and competence of the flow, but robust definitions of these terms have proved elusive. In this paper we provide a mathematical modeling framework within which erosion and deposition of polydisperse sediment, and thus flow capacity and competence, can be rigorously defined. This framework explicitly captures the coupling between the suspension and an active layer of sediment at the top of the bed, and is capable of describing both depositional and erosional flows over both erodible and nonerodible beds. Crucially, the capacity of a flow is shown to depend on the erosional and depositional history because these processes determine the composition of the active layer. This dependence is explored within models of bidisperse and polydisperse suspensions. It is further demonstrated that monodisperse representations of suspended sediment transport may severely underpredict actual flow capacity. The polydisperse model is validated against recent experimental studies of the evolution of suspended material in waning turbulent flows, and is used to demonstrate that loss of capacity is the principal driver of sediment deposition.