This is the first paper in a four-part sequence exploring the factors that govern the distribution of pelagic sediments in regions of the world mid-ocean ridge system where basement outcrops and sediment deposits both contribute to local topography. In this paper, we present a simple numerical model of pelagic sedimentation in which sediments travel from topographic highs to lows, with flux regulated by a diffusivity parameter &kgr;. By applying the forward model to realistic models of basement topography we investigate how various basement structures, sediment rain rates, and values of &kgr; affect the morphology of the seafloor through time. We quantify the effect of sedimentation as a nonlinear smoothing filter on topography, which acts to reduce spectral power at high wavenumber, to decrease the root-mean-square variability of topography, to increase the spacing between hills, and to lower the relative proportion of high-slope seafloor. We find that local accumulation rate is highly dependent on local topography and varies greatly with time. We also find that sediment compaction does not contribute directly to the surface concavity exhibited by many intrahill sediment ponds. ¿ 2001 American Geophysical Union