In this work we study hydrogen isotope fractionation along the proposed gas-phase ammonia formation pathway at temperatures relevant to interstellar modelling. Specifically we study the isotopically substituted variants of the NH(+) + H(2) reaction, for which the primary product is NH(2)(+) + H. Adiabatic capture theory calculations have been performed for the association reaction. A new potential-energy surface has been determined for the NH(2)(+) product. An extensive set of rovibrational energy levels has been calculated for the NH(2)(+) isotopologues described by this potential-energy surface. These rovibrational energy levels have been used to determine energy- and angular-momentum-resolved numbers of accessible product states from the NH(3)(+) isotopologue intermediates, which in turn have been averaged to give statistical branching fractions for all isotopically-substituted NH(+) + H(2) reactions. It is determined that in all cases where both hydrogen and deuterium are present, the NHD(+) product is preferred.