A liquid-state theory is presented for the conformational properties and intermolecular structure of concentrated solutions and bulk melts of purely repulsive star-branched polymers. The theory generalizes earlier work on linear chains and is based on a solvation potential, expansion of the single-chain free energy to second order in monomer interactions, and interaction-site integral equation theory. Information about the chemical structure of polymers, in particular intra- and intermolecular interaction potentials with a finite excluded volume per monomer, may be included straightforwardly. The theory does not assume incompressibility in the melt and suffers no loss of accuracy in the short-chain, small-arm-number limit. Also presented here is a study of conformational properties, including radius of gyration, mean arm end-to-end distance, monomer density profile, and local persistence length, for concentrated solutions and melts of a hard-sphere, branched-pearl-necklace model of star polymers with a moderate (4-12) number of arms. Stretching of the star arms near the branch point is found, and a concomitant swelling of the star with respect to the fully ideal state is predicted, even at meltlike densities and even in the few-arm limit. Measures of the swelling are compared with experimental measurements, the Daoud-Cotton "blob" model, and the "exclusion zone" model of Boothroyd and Ball. The physical origin of the stretching is also discussed in detail.