The topology and morphology of the free surface of styrene-butadiene diblock copolymers were investigated by transmission electron microscopy as functions of molecular weight, composition, diene configuration, casting solvent and solvent evaporation rate. It was found that in solvent-cast thick films the formation of equilibrium free surface depends on a delicate balance of kinetic and thermodynamic parameters. Fast evaporation rates induce orientation of lamellar and cylindrical microdomains perpendicular to the free surface, while slow rates produce equilibrium-like domain orientation, parallel to the free surface. Molecular mechanisms of such arrangements are discussed, and it is concluded that to rapidly obtain an equilibrium free surface, the difference between critical surface tensions of polystyrene (PS) and polybutadiene blocks must be the greater the higher the affinity between the casting solvent and the block (PS) with the higher critical surface tension.