Physical and numerical modeling of fluviodeltaic depositional systems, conducted under constant conditions of relative sea-level fall, sediment discharge, and water discharge, demonstrates that "sustained" alluvial aggradation is the inherent stratigraphic response of alluvial rivers that are steeper than the receiving basin. High alluvial gradients are primarily a consequence of high sediment supply relative to available water discharge (low rate of terrestrial diffusion). During the course of the experiments, fluvial grade was never reached, fluvial incision was never observed, and aggradation occurred independently of shoreline position. The experiments revealed detachment of the shoreline from the alluvial river as an autogenic response of certain fluviodeltaic systems to steady relative sea-level fall, creating a "non-deltaic" alluvial-river system that continues to aggrade beyond shoreline detachment. We term this behavior "autodetachment." Autodetachment is a consequence of sustained, extensive alluvial aggradation during relative sea-level fall. Sediment supply was increasingly partitioned into the ever-enlarging alluvial profile to the detriment of the delta front prior to shoreline detachment. Thus, as relative sea level fell, the length of the delta front decreased to zero. Simultaneously, alluvial aggradation also led to decreasing rates of delta progradation. Therefore, as the delta front disappeared, the rate of shoreline regression exceeded the rate of progradation, producing a "bedrock" river between the detached alluvial river and the shoreline. The Canterbury Plains of New Zealand is a natural-world system with alluvial gradient greater than shelf gradient. Geometric modeling suggests that autodetachment could have occurred at the Canterbury Plains within the timescale of Quaternary glacio-eustatic sea-level falls, and therefore, is a realistic stratigraphic response at the scale of natural-world systems. Our model demonstrates that deltas with these geometric parameters become poorly supplied during regression, and large lowstand deltas should not be expected for these types of systems. The results of this study complement existing autostratigraphic theory, and provide an alternative to allogenic drivers for geomorphic and architectural evolution of fluviodeltaic wedges.