Eustasy constitutes a key control on continental-shelf accommodation along with tectonism. The combined effect of these processes influences relative sea level, which is thought to regulate the location of facies, stratigraphic architecture, and distribution of sediment to basin margins. Here, we used a nonlinear, diffusion-based, numerical stratigraphic forward model to investigate the impact of the eustatic curve. We ran two models, one using a eustatic curve derived from the New Jersey margin, U.S.A., and the other a base case with no eustatic variation, but which were otherwise identical. We conclude that changing the eustatic curve resulted in a 0.9 % difference in cumulative deep water (≥ 200 m) sand volumes between models. This is because the no eustatic variation model resulted in deep-water sand delivery events with magnitudes similar to those observed in the eustatic model which were due to the delta becoming fixed at the shelf edge and the subsequent temporary suspension of avulsive processes. In the eustatic model, maximum deep-water sand accumulation occurred during short-term sea-level falls, but peak sand delivery was not well-related to the amplitude of the sea-level fall itself. Further examination of the relationship between rates of relative sea level and deep-water sand delivery show a poor correlation (r2 < 0.1). This suggests that delta equilibrium state and autogenic processes such as avulsion introduce an element of unpredictability to the transport of sand across the shelf into deep water. Additionally, the result of autogenic and allogenic processes may be indistinguishable in the geologic record.