The theory of the kinetics of binding of ligands to a sphere partially covered by receptors is extended to provide the full time dependence of the reactive flux. The ligands diffuse to the receptors; the receptors are either fully or partially absorbing. The total flux into the sphere with many receptors is expressed analytically in terms of the flux into a single isolated receptor on the sphere. At steady state, the Berg-Purcell formula is generalized to the case where the binding to a single receptor is only partially diffusion controlled. At short times, the receptors behave independently and the total flux is the sum of the fluxes to the isolated receptors.