Using an off-lattice bead-spring model of flexible polymer chains containing N = 32 beads under bad solvent conditions, thin films of polymer melts are simulated. The films are confined between two parallel plates, the upper plate being purely repulsive while the lower plate exerts a short range attraction on the polymer layer so that a dense thin film is adsorbed on this plate for large enough attraction strength epsilon. Then "quenching experiments" are simulated by suddenly reducing epsilon at time t = 0 and monitoring the time evolution of the polymer film. While for large enough final values of epsilon only the density in the film decreases somewhat, but the film stays laterally homogeneous, for epsilon less than a critical value epsilon(c) it is found that the film breaks up into droplets. The early stages of the time evolution of this process in the framework of a dynamic Monte Carlo simulation are studied both by recording the time dependence of the adsorbed amount, the average thickness of the layer, the distribution function of meansquare displacements, and with the help of snapshot pictures of the system configurations. Also equilibrium properties of the films are investigated including both collective properties such as density profiles and radial distribution functions, and single-chain properties such as parallel and perpendicular parts of meansquare gyration radii, in dependence on the adhesive strength epsilon of the substrate.