We propose a theory of nanopattem formation in ultrathin films obtained by the spreading of A-B diblock copolymers on a surface. A blocks are strongly adsorbed (spread) on the substrate, and the strength of the adsorption can be varied. B blocks are incompatible with the substrate, but they can spread atop the layer of the A blocks. We predict disk-shaped micelles ordered with hexagonal symmetry and parallel stripe-shaped micelles and bilayers to be stable. The type of resulting structure and its geometrical parameters depend on the composition of the copolymer and interaction parameters. We interrelate these results with those obtained for the case of the spreading of both blocks on the substrate,(19) and we construct a unified phase diagram.