  We study a class of zero-range processes in which the real-space condensation
phenomenon does not occur and is replaced by a saturated condensation: that is,
an extensive number of finite-size "condensates" in the steady state. We
determine the conditions under which this occurs, and investigate the dynamics
of relaxation to the steady state. We identify two stages: a rapid initial
growth of condensates followed by a slow process of activated evaporation and
condensation. We analyze these nonequilibrium dynamics with a combination of
meanfield approximations, first-passage time calculations and a
fluctuation-dissipation type approach.
