We use scaling arguments and self-consistent field calculations to determine the behavior of AB diblock copolymers that are grafted to a planar surface at relatively low densities. The surrounding solution is assumed to be a theta or marginally good solvent for the A block and a poor solvent for the B block. When the chains are grafted by the ends of the B blocks and the B blocks are sufficiently long, the layer associates into an ordered array of "flowerlike" structures. The solvophobic B’s form the core of the "flowers", and the soluble A’s form the outer corona of "petals". The size and spacing of the micellar aggregates can be manipulated by varying the different block lengths. The findings provide guidelines for fabricating patterned films with well-defined morphologies.