Recent experiments on the abstraction of D adsorbed on metal surfaces with gaseous hydrogen atoms revealed a kinetics of HD formation which is not compatible with the operation of Eley-Rideal (ER) mechanisms. Furthermore, homonuclear products were observed during abstraction, which are not expected through an ER reaction scheme. It was therefore suggested that hot-atom (HA) mechanisms are more appropriate to explain the measured kinetics and products. Random walk calculations of the abstraction kinetics are presented based on a model which exclusively relies on elementary reaction steps which are HA mediated processes. Within this model, the ratio of two variables, the probabilities for hot-atom sticking at empty sites p(s) and hot-atom reaction with adsorbed species p(r), was found to control the kinetics of HD and D-2 formation. The essential features of measured kinetic data at Ni(100), Pt(lll), and Cu(lll) surfaces were reproduced by simple and reasonable assumptions on p(s)/p(r).