By comparing two models for the transport of sediment, we find that they share a similar steady-state solution that adequately predicts the shape of most depositional systems made of a fan and an alluvial plain. The length of the fan is controlled by the size of the mountain drainage area feeding the sedimentary system and its slope by the incoming sedimentary flux. We show that the models differ in their transient behavior to external forcing and are characterized by different response times.