Aims. We seek to study the abundances of H 2 , HD, and D 2 adsorbed onto ice-covered dust grains in dark molecular clouds in the interstellar medium. Methods. We use our previously developed detailed model describing temperature-programmed desorption (TPD) experiments of H 2 and its isotopologues on water ice. We here extrapolate these model results from laboratory conditions to conditions similar to those found in dark molecular clouds. Results. By means of our model we are able to infer three

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... important results. (i) The time scale for H 2 and isotopologues to accrete onto dust grains is less than 10 4 yrs. (ii) Due to the higher binding energy of D 2 with respect to HD, D 2 becomes the most abundant deuterated species on grains by ∼50% with respect to HD (a few times 10 −5 with respect to H 2 ). (iii) The surface coverage of D 2 as a function of temperature shows that at very low temperatures (i.e., less than 10 K), D 2 may be two orders of magnitude more abundant than HD. Possible implications for deuteration of water on grain surfaces are discussed when it forms through reactions between OH and H 2 .