Asymmetric diblock copolymers with a spherical domain structure form islands or holes on the free surface of a thin film when the initial spun-cast film thickness does not match that of an integral number of layers of spheres plus a brush. When this film is cast on a substrate topologically patterned with rectangular, flat bottomed wells as deep as a layer of spheres, the edges of these wells act as sinks for excess material. As a result, we observe the movement of material away from the raised areas (mesas) toward the adjacent wells so that if a mesa surface initially contains holes exposing the underlying layer of spheres or brush, these holes will coalesce and grow until the top layer of spheres forms a bicontinuous structure with the holes, and finally this structure will break up into discrete islands. If the islands exist on top of only a brush layer, their shrinkage is limited by the detachment kinetics of a chain from the island into the brush. If the islands are on top of another layer of spheres, the shrinkage of the islands is much faster than would be expected if it were controlled by the diffusion of chains through the underlying nanodomain structure.