We present the results of quasiclassical trajectory studies of the H + H2O --> OH + H-2, H + D2O --> OD + HD, and H + D2O --> D + HOD reactions. The new potential energy surface of Ochoa and Clary (J. Phys. Chem. A. 1998, 102, 9631) derived from ab initio calculations has been employed. Absolute reaction cross sections as a function of collision energy have been calculated and compared with previous experimental and theoretical results. Our calculations are in qualitative agreement with the experimental determinations. Additionally, vibrational and rotational distributions have been calculated and compared with experimental measurements. The calculations reproduce the low vibrational excitation for OH and OD products and the relatively cold rotational distributions for OH, OD, and IID products observed ill the experiments.