We investigate the density profile of diblock-copolymer melts and polymer blends close to a patterned surface. For diblocks we find a dependence of the orientation of the polymer chains and the lamellae on the ratio of the natural bulk period to the pattern period L. For a very large pattern period, the diblocks experience locally a homogeneous surface and orient perpendicular to it. For commensurable periods, their orientation is parallel and the lamellae are perpendicular to the surface. A sudden change in orientation is seen at a ratio R-g/L=root 2 root 3/2 pi for symmetric diblocks, where R-g is the radius of gyration of the diblock in the disordered melt. Polymer blends always follow the surface pattern close to the surface if the surface interaction is strong enough. (C) 1997 American Institute of Physics.