The flow of an unmagnetized plasma produced by ion beam pulses impinging on spherical targets is considered. The analysis, which allows for variable ionization degree, radiation transport, and the effect on the stopping power of both free and bound electrons, shows the existence of two distinguished limits in the flow behaviour: the ablation and heating regimes. For the ablative quasi-steady expansion the analysis yields the ablation pressure and the ablated mass rate as a function of the beam parameters (beam energy per nucleon Eb and current intensity Ib); radiation transport is found to be negligible in this regime. The results may be used for determining the beam energy history Eb(t), for a given Ib(t), (or Ib(t) for Eb(t) given) required to generate a given law ablation pressure Pa(t) on an ablation surface R(t). The heating regime, which develops for too intense and short ion beam pulses, is studied using perturbation methods; profiles of beam velocity and plasma temperature are obtained from the analysis.