  The availability of collisional rate coefficients is a prerequisite for an
accurate interpretation of astrophysical observations, since the observed media
often harbour densities where molecules are populated under non--LTE
conditions. In the current study, we present calculations of rate coefficients
suitable to describe the various spin isomers of multiply deuterated ammonia,
namely the ND$_2$H and ND$_3$ isotopologues. These calculations are based on
the most accurate NH$_3$--H$_2$ potential energy surface available, which has
been modified to describe the geometrical changes induced by the nuclear
substitutions. The dynamical calculations are performed within the
close--coupling formalism and are carried out in order to provide rate
coefficients up to a temperature of $T$ = 50K. For the various
isotopologues/symmetries, we provide rate coefficients for the energy levels
below $\sim$ 100 cm$^{-1}$. Subsequently, these new rate coefficients are used
in astrophysical models aimed at reproducing the NH$_2$D, ND$_2$H and ND$_3$
observations previously reported towards the prestellar cores B1b and 16293E.
We thus update the estimates of the corresponding column densities and find a
reasonable agreement with the previous models. In particular, the
ortho--to--para ratios of NH$_2$D and NHD$_2$ are found to be consistent with
the statistical ratios.
