The desorption of molecular ices from grain surfaces is important in a number of astrophysical environments including dense molecular clouds, cometary nuclei and the surfaces and atmospheres of some planets. With this in mind, we have performed a detailed investigation of the desorption of pure water, pure methanol and pure ammonia ices from a model dust-grain surface. We have used these results to determine the desorption energy, order of desorption and the pre-exponential factor for the desorption of these molecular ices from our model surface. We find good agreement between our desorption energies and those determined previously; however, our values for the desorption orders, and hence also the pre-exponential factors, are different to those reported previously. The kinetic parameters derived from our data have been used to model desorption on time-scales relevant to astrophysical processes and to calculate molecular residence times, given in terms of population half-life as a function of temperature. These results show the importance of laboratory data for the understanding of astronomical situations whereby icy mantles are warmed by nearby stars and by other dynamical events.