Surface-pattern formation in thin block copolymer films was investigated by utilizing a high-throughput methodology to validate the combinatorial measurement approach and to demonstrate the value of the combinatorial method for scientific investigation. We constructed measurement libraries from images of subregions of block copolymer films having gradients in film thickness and a range of molecular mass, M. A single gradient film covers a wide range of film morphologies and contains information equivalent to a large number of measurements of films having a fixed thickness, h. Notably, the scale of the surface patterns is generally much larger than the molecular dimensions so that the interpretation of the patterns is more subtle than ordering in bulk block copolymer materials, and there is no predictive theory of this type of surface-pattern formation. We observed a succession of surface patterns that repeat across the film with increasing h [extended smooth regions, regions containing circular islands, labyrinthine ("spinodal") patterns, holes, and smooth regions again]. The extended smooth regions and the labyrinthine patterns appear to be novel features revealed by our combinatorial study, and these patterns occurred as bands of h that were quantized by integral multiples of the bulk lamellar period, L-o. The magnitude of the height gradient influenced the width of the bands, and the smooth regions occupied an increasing fraction of the film-surface area with an increasing film gradient. The average size of the spinodal patterns, lambda, was found to scale as lambda similar to L-o(- 2.5) or lambda similar to M-1.65 and reached a limiting size at long annealing times. The hole and island features had a size comparable to lambda, and their size likewise decreased with increasing M. The smooth regions were attributed to an increase in the surface-chain density in the outer brushlike block copolymer layer with increasing h, and the scaling of lambda with M was interpreted in terms of the increasing surface elasticity with M.