Continental shelves and coastal plains are large persistent depositional landforms, which are stationary (nonmigrating) at their proximal ends and characterized by relatively steady long-term growth. In detail, however, their surface form and stratigraphic record is built of transient freely migrating landscape elements. We derive the timescales of crossover from transient to persistent topographic forms using empirical scaling relations for mean sediment accumulation as a function of averaging time, based upon tens of thousands of empirical measurements. A stochastic (noisy) diffusion model with drift predicts all the gross features of the empirical data. It satisfies first-order goals of describing both the surface morphology and stratigraphic completeness of depositional systems. The model crossover from noise-dominated to drift-dominated behavior corresponds to the empirical crossover from transport-dominated (autogenic) transient behavior to accommodation-dominated (subsidence) persistent behavior, which begins at timescales of 102–103 years and is complete by scales of 104–105 years. Because the same long-term scaling behavior emerges for off-shelf environments, it is not entirely explicable by steady subsidence. Fluctuations in sediment supply and routing probably have significant influence. At short-term (transient) scales, the exponents of the scaling relations vary with environment, particularly the prevalence of channeled sediment transport. At very small scales, modeling sediment transport as a diffusive process is inappropriate. Our results indicate that some of the timescales of interest for climate interpretation may fall within the transitional interval where neither accommodation nor transport processes are negligible and deconvolution is most challenging.