The migration of water molecules across the lunar surface from sources sufficiently small, so as to not generate a transient collisional atmosphere, was examined using a Monte Carlo simulation. Previous work using similar models is extended by examining a realistic distribution of large south polar Permanently Shadowed Regions (PSRs) to examine the heterogeneities observed in their water content-frost in Haworth and the nearby lowlands, but not in neighboring Shoemaker, and anomalously high hydrogen abundances from neutron data-and to determine how the pattern of water delivery can be distinguished from that predicted for transient collisional atmospheres. While the Haworth lowlands were seen to accumulate 3.9 times as much water as Shoemaker, the additional water delivered to Haworth crater was only 47% greater than Shoemaker, possibly due to shielding by Faustini and the lowlands. This relatively small difference is likely inadequate to explain the difference in frosting. More broadly, latitudinal trends in delivery dominate over meridional trends. Despite the heterogeneity in water delivery, fractionation effects from ballistic migration were small for the PSRs with equal D/H ratios seen in all PSRs within confidence limits. Finally, a diffusive barrier was observed starting at approximately 15°from each pole that hampers the poleward progress of equatorial particles. This barrier is the result of a reduction in the migration diffusivity from 1.0 × 10 7 m 2 s À1 near the equator to 5.5 × 10 5 m 2 s À1 within 10°of the pole and finally to 6.8 × 10 3 m 2 s À1 within 4°of the pole.Values for solar wind-derived water are more difficult to ascertain. Recent summary work, such as Basilevsky et al.[2012] still cite early estimates, such as those of Arnold [1979] which indicate that of order 10 14 kg of water might be generated over the past 2 Ga via this mechanism. However, it is not well known how much MOORES PSR BALLISTIC MIGRATION HETEROGENEITY 46 PUBLICATIONS