The relaxation properties of the Euler-Poisson flow with spherical symmetry are studied. For smooth and small initial data, the existence of global smooth solutions is proved. This indicates that the frictional dissipation from the relaxation term can prevent the formation of singularities in small smooth solutions of the Euler-Poisson flow with spherical symmetry. The zero relaxation limit of the general large weak entropy solutions is established. The convergence of the scaled solutions to the solution of a generalized drift-diffusion equation as the relaxation tends to zero is proved.