Non-LTE (Local Thermodynamical Equilibrium) modeling implies competition between radiative and collisional processes. The influence of inelastic hydrogen atoms collisions, dominant in cold atmospheres has been and remains to be a significant source of uncertainty for stellar abundance analysis. In the particular case of Mg atoms, a large number of electronic states of the MgH molecule as well as the associated couplings that mix the states during the collision were calculated by high level quantum chemical methods and then used in full quantum scattering calculations. This allows to treat the excitation processes between the seven lowest atomic states of magnesium in collision with hydrogen atoms, as well as the ion-pair production and the mutual neutralization processes. The detailed mechanisms involved during the collision process have been analysed in detail. Our calculations show that the usual approximate Drawin formula leads to errors by factors up to 10(5). As was already found in Li+H and Na+H collisions, excitation processes were found to be less important than charge transfer processes. However, unlike Li and Na, Mg has different spin terms, singlet and triplet, leading both to doublet molecular MgH electronic states. Collisional rates between spin-allowed and optically spin-forbidden atomic states are found to be of the same order of magnitude although optically spin-forbidden states are only collisionally coupled. Thus we may expect consequences on non-LTE calculations.