We examine the phase diagram of starblock copolymers with monodisperse diblock arms. Within a self-consistent-field theory, we calculate the phase diagrams for starblocks with equal Kuhn lengths for all monomers, and M = 1, 3, 5, and 9 arms. For M = 1 and 5, we also consider the effect of asymmetric Kuhn lengths. We find all phase diagrams to be topologically identical to that of diblocks (M = 1). In each case, the lamellar, gyroid, hexagonal, and cubic phases are found to be stable. The region of stability of the gyroid phase is found to increase as the number of arms is increased. Regions in which the double-diamond and catenoid-lamellar phases are nearly stable are also located.