By Monte Carlo simulation of two lattice models of polymer melts, the enrichment of the chain ends in the vicinity of a wall is obsserved. For the bond fluctuation model with attractive interactions between the ends and wall, ε/kB T=-1 and 0, the enhancement of the density of ends increases with chain lengths, while when the interaction is repulsive, ε/kB T=+1, the ends get depleted. The self-avoiding walk model was simulated with the slithering snake algorithm and behaves similarly. The polymer center of mass density profile, radius of gyration and end-to-end distance components parallel and perpendicular to the wall as functions of center of mass distance z scale with Rg, where Rg is radius of gyration of the polymer chains in the bulk