Intraslope basins, or minibasins, are topographic features of the continental slope that can be filled with sediment transported by submarine flows. These deposits may contain important hydrocarbon reservoirs. Here we present results of two-dimensional numerical simulations of multiple turbidity currents entering two linked minibasins. The numerical model accounts for the non-uniformity of sediment grain size in the flow and the resulting deposit. Model results reasonably reproduce the evolution of linked minibasins illustrated in the field based “fill-and-spill” conceptual model. The conceptual model was developed for the Brazos–Trinity system from field observations. Further, simulations of two linked minibasins show that the upstream basin traps most of the coarse sediment. This material is deposited in the proximal zone of the basin and fine sediment is transported farther downslope, resulting in the formation of a weak pattern of downstream fining. Model results with different initial and boundary conditions reveal that minibasin geometry and turbidity-current characteristics are important controls on the deposit shape and grain-size distribution.