The behaviour of star polymers adsorbed on smooth surfaces is studied using coarse-grained bead-spring models and Langevin dynamics simulations. The conformational properties of a single adsorbed star polymer in good-solvent conditions are considered as functions of the functionality (number of arms) f, the number of monomers per arm N, and the monomer-surface interaction energy epsilon(s). Four conformational regimes are identified: a linear-polymer regime; a two-dimensional star polymer regime; a sombrero regime; and a colloidal regime. The latter three correspond to regimes predicted theoretically by Halperin and Joanny [J. Phys. II (France), 1991, 1, 623-636]. Solvent effects are explored by dialing in effective attractions between the monomer beads; with decreasing solvent quality, the star polymers adopt more compact, globular structures. Good-solvent to bad-solvent quenches at finite surface coverages are considered; these correspond to established experimental protocols for adsorbing and then drying polymer sub-monolayers on surfaces. The structure of the polymer film is surveyed as a function of surface coverage, f, N, and epsilon(s), in good-solvent and bad-solvent conditions. The simulated post-quench structures are in good qualitative agreement with those observed in atomic-force microscopy measurements, while the simulated pre-quench structures shed light on the microscopic mechanisms of film formation. This study draws together much of what is known about surface-adsorbed star polymers from theory, simulation, and experiment.