Simulation calculations are reported for single-chain polymer-wall conformation-averaged potentials of mean force and segment-density profiles for homopolymers of different structures as a function of the segment-wall attractive potential. When there is no attraction between the wall and the polymer segments, the presence of the wall generates a polymer-segment depletion layer whose thickness depends on polymer structure and on surface roughness. Segment-density profiles are characterized by three regions. In the proximal region, the segment density is determined by surface roughness and by polymer flexibility. In the distal region, the segment density approaches unity asymptotically. In the central region, the segment density depends on geometric characteristics of the polymer in the bulk solution. When the wall-segment attractive potential is sufficiently large, the depletion layer thickness is reduced and the polymers are adsorbed. When attraction is weak, compact polymers (e.g., dendrimers of high generation) are readily adsorbed. Due to their globular shape, high-generation dendrimers, at weak attractive interactions, are at contact with the surface with numerous segments; globular polymers experience a relatively small entropic penalty for adsorption. By contrast, linear polymers, due to their flexibility at good solvent conditions, pay a high entropic penalty for each segment at contact with the surface. Therefore, at weak attractive interactions, globular polymers are readily adsorbed, whereas linear polymers are more readily adsorbed at stronger attractive interactions. With rising surface roughness, flexible polymers tend to spread on the surface, whereas branched polymers are repelled at larger distances.