We studied by lattice simulation the surface diffusion and relaxation of isolated, self-avoiding polymers partially adsorbed onto a flat surface. The key parameters describing the system are the number of segments in the chain, N, the adsorption energy of a segment, expressed as a dimensionless surface temperature T-s, and the segmental friction factor on the surface relative to that in the hulk, zeta(s)/zeta(b). The simulation data indicate Rouse scaling of the surface diffusion coefficient, D-parallel to, and in-plane relaxation time, tau, versus N for all values of T-B and zeta(s)/zeta(b) studied. A simple application of the Rouse model to a partially adsorbed chain, which ignores fluctuations in adsorbed trains, yields a formula for D-parallel to with the correct N-scaling. It can account for the effects of T-s when zeta(s)/zeta(b) is finite (less than or similar to 10), but it fails when zeta(s)/zeta(b) diverges, predicting no surface diffusion at all, whereas simulations indicate finite surface mobilities facilitated by a caterpillar-like motion.