We use scaling arguments to determine the patterns that form when Y-shaped AB copolymers are grafted onto a flat surface. One "arm" of the Y is an A homopolymer, and the other arm is an incompatible B chain, and the short "stem" tethers the entire copolymer to the surface. We investigate the behavior of the brush formed from these chains in the melt and in the presence of a solvent. In particular, we determine how solvent quality, grafting density, and chain length affect the structure of the grafted layer. We then calculate a phase diagram that delineates the regions where the different structures appear. The diagram reveals that variations in the solvent quality give rise to a rich variety of lateral structures. The results provide guidelines for fabricating patterned or highly ordered thin films.