We investigate spreading of phase separated copolymer films, where domain walls and thickness steps influence polymer flow. We show that at early stages of spreading its rate is determined by slow activated flow at terrace steps (i.e., thickness steps). At late stages of spreading, on the other hand, the rate is determined by the flow along terraces, with diffusionlike time dependence t(-1/2). This dependence is similar to de Gennes and Cazabat's prediction for generic layered liquids [P. G. de Gennes and A. M. Cazabat, C.R. Acad. Sci. Paris II 310, 1601 (1990)], as opposed to the classical Tanner's law of drop spreading. We also argue that chain hopping at the spreading terrace steps should lead to the formation of aligned, defect-free domain patterns on the growing terraces. (C) 2004 American Institute of Physics.