Molecular dynamics (MD) simulations have been performed on a dense polymer melt adsorbed on a solid substrate on the one side and exposed to vacuum on the other. As a model system, a thin film of polyethylene (PE) melt supported by a crystalline graphite phase on its one side (the other surface of the film is free) has been examined. Most simulations have been carried out with unentangled PE melt systems, such as C-78 and C-156, in the NPT statistical ensemble at T = 450 K and P = 0 atm for times up to 100 ns, using a multiple-time step MD algorithm and by incorporating the correct dependence of the long-range contribution to the energy and stress tensor on the density profile. To increase the statistical accuracy of the results, large systems have been employed in the MD simulations, such as a 200-chain C-78 melt consisting of 15 600 carbon atoms. The MD simulation data have been analyzed to provide information about the spatial dependence of the short-time dynamical properties (conformational relaxation) of the melt and the long-time segmental motion and mobility in the film (transport and diffusion). Local mobility near the graphite phase is predicted to be highly anisotropic: although it remains practically unaltered in the directions x and y parallel to the surface, it is dramatically reduced in the direction z perpendicular to it. To calculate the long time self-diffusion coefficient of adsorbed segments in the direction perpendicular to the graphite plane, MD trajectories have been mapped onto the (numerical) solution of a macroscopic, continuum diffusion equation describing the temporal and spatial evolution of the concentration of adsorbed atoms in the polymer matrix. Our calculations prove that the diffusive motion of segments remains inhomogeneous along the z direction of the adsorbed film for distances up to approximately 5-6 times the root-mean-square of the radius of gyration, R-g, of the bulk, unconstrained melt.