  Super-Earths orbiting M-dwarf stars may be the most common habitable planets
in the Universe. However, their habitability is threatened by intense
irradiation from their host stars, which drives the escape of water to space
and can lead to surface desiccation. We present simulation results of a box
model of water cycling between interior and atmosphere and loss to space, for
terrestrial planets of mass 1--8 $M_\oplus$ orbiting in the habitable zone of a
late M-dwarf. Energy-limited loss decreases with planetary mass, while
diffusion-limited loss increases with mass. Depending on where it orbits in the
habitable zone, a 1 $M_\oplus$ planet that starts with 3--8 Earth Oceans can
end up with an Earth-like surface of oceans and exposed continents; for an 8
$M_\oplus$ super-Earth, that range is 3--12 Earth Oceans. Planets initialized
with more water end up as waterworlds with no exposed continents, while planets
that start with less water have desiccated surfaces by 5 Gyr. Since the mantles
of terrestrial planets can hold much more water than is currently present in
Earth's atmosphere, none of our simulations result in Dune planets -- such
planets may be less common than previously thought. Further, more water becomes
sequestered within the mantle for larger planets. A super-Earth at the inner
edge of the habitable zone tends to end up as either a waterworld or with a
desiccated surface; only a narrow range of initial water inventory yields an
Earth-like surface.
