  Most studies suggest the pollution of white dwarf (WD) atmospheres arises
from accretion of minor planets, but the exact properties of polluting
material, and in particular the evidence for water in some cases are not yet
understood. Here we study the water retention of small icy bodies in exo-solar
planetary systems, as their respective host stars evolve through and off the
main sequence and eventually become WDs. We explore for the first time a wide
range of star masses and metallicities. We find that the mass of the WD
progenitor star is of crucial importance for the retention of water, while its
metallicity is relatively unimportant. We predict that minor planets around
lower-mass WD progenitors would retain more water in general, and would do so
at closer distances from the WD, compared with high-mass progenitors. The
dependence of water retention on progenitor mass and other parameters has
direct implications for the origin of observed WD pollution, and we discuss how
our results and predictions might be tested in the future as more observations
of WDs with long cooling-ages become available.
