We numerically study morphology of thin diblock copolymer films as a function of the relative size or the "composition" f of the shorter block of the copolymer chains. We probe various values of f, spanning the whole bulk phase diagram of asymmetric diblock copolymers. Finite size of the film and wetting properties of the substrate modify the film morphology by shifting the effective value of the composition f in the film. A dramatic change in film morphology takes place for a small change in external parameters if one chooses the composition f to be at the borderline between two different bulk phases. (C) 2003 American Institute of Physics.