We report a large set of state-to-state rate constants for the H + HD reactive collision, using Quasi-Classical Trajectory (QCT) simulations on the accurate H 3 global potential energy surface of Mielke et al. [J. Chem. Phys. 116, 4142 (2002)]. High relative collision energies (up to ≈56 000 K) and high rovibrational levels of HD (up to ≈50 000 K), relevant to various non thermal equilibrium astrophysical media, are considered. We have validated the accuracy of our QCT calculations with a new efficient adaptation of the Multi Configuration Time Dependent Hartree (MCTDH) method to compute the reaction probability of a specific reactive channel. Our study has revealed that the high temperature regime favors the production of H 2 in its highly rovibrationnally excited states, which can de-excite radiatively (cooling the gas) or collisionally (heating the gas). Those new state-to-state QCT reaction rate constants represent a significant improvement in our understanding of the possible mechanisms leading to the destruction of HD by its collision with a H atom.