  We study the quantum evolution of black holes immersed in a de Sitter
background space. For black holes whose size is comparable to that of the
cosmological horizon, this process differs significantly from the evaporation
of asymptotically flat black holes. Our model includes the one-loop effective
action in the s-wave and large N approximation. Black holes of the maximal mass
are in equilibrium. Unexpectedly, we find that nearly maximal quantum
Schwarzschild-de Sitter black holes anti-evaporate. However, there is a
different perturbative mode that leads to evaporation. We show that this mode
will always be excited when a pair of cosmological holes nucleates.
