One of the surprises of the NEAR-Shoemaker mission was that Eros's surface exhibits a wide variety of landforms, which are indicative of a global covering of loose fragmental debris. At one extreme in roughness is the Shoemaker Regio area, which is characterized by a high density of boulders up to 100 m across, slumps, slides, and finer blanketing material. At the other extreme are distinctive, flat deposits that appear smooth down to a resolution of 1.2 cm per pixel. Here we report the results of global mapping and colour analysis of these smooth deposits. They have formed most efficiently in restricted areas, and appear to be the result of deposition of finer material sorted from the upper portion of the asteroid's regolith. The smooth deposits constitute a family of features with a range of morphologies, but all appear to be the result of sedimentation. The geography of the deposits is consistent with some predicted aspects of photoelectric sorting, but these exotic transport and depositional mechanisms are not well understood. Deposits with the properties seen on Eros have no obvious analogues in previous lunar or asteroid data.