We study a lattice model of an interacting uniform self-avoiding star polymer with f branches. A 1/d -expansion for the limiting reduced free energy is derived through order 1/d for general f and, for f = 3, to order 1/d ² . The terms in the expansion are independent of f and agree term by term with the corresponding expansion for interacting self-avoiding walks. We also present a miscellany of numerical results obtained by more conventional series and Monte Carlo techniques. All our results, both past and present, support the conjecture that the limiting reduced free energies of f -stars, walks and polygons are identical for all values of the interaction parameter .