The closeup images of Hyperion obtained by Voyager 2 show features diagnostic of a catastrophic impact event which disrupted a parent satellite. The irregular shape of the present Hyperion suggests that the fragments formed in this impact could not reaccrete, because their ejection velocity exceeded the parent's escape velocity and resulted within a short time in a sequence of close approaches to Titan. This process may have occurred as an outcome either of chaotic dynamics associated with the 4:3 mean motion resonance with Titan or of initial ejection velocities of several hundred meters per second. As a consequence, the fragments either impacted Titan or spread into the inner part of the Saturnian system and contributed to the cratering record of the inner satellites. In this paper we estimate, by simple dynamical models based on E.J. Öpik's theory (Interplanetary Encounters, Elsevier, Amsterdam, 1976), the relative probabilities of the various outcomes of this evolution. Our models predict that in fact the vast mojority of fragments were swept up by Titan, so that the flux of impactors declined rapidly inward, and apart from Rhea it was very low for all the inner satellites. The younger crater Population II, recognizable in the Voyager images of the inner satellites, does not show the sharp gradient with planetocentric distance and the systematic leading-trailing asymmetry predicted if the impactor source had been Hyperion's breakup. In the particular case of Rhea, however, there is some evidence of a leading-trailing asymmetry in the available data on crater densities, and the models predict that the flux from a proto-Hyperion of reasonable size may have been intense enough to produce a significant total cratered area. Moreover, the very short and intense bombardment episode predicted for Titan may have affected its atmospheric composition and/or surface features. © 1990.