  We calculate the one-loop effective action for conformal matter (scalars,
spinors and vectors) on spherically symmetric background. Such effective action
(in large $N$ approximation and expansion on curvature) is used to study
quantum aspects of Schwarzschild-de Sitter black holes (SdS BHs) in nearly
degenerated limit (Nariai BH). We show that for all types of above matter SdS
BHs may evaporate or anti-evaporate in accordance with recent observation by
Bousso and Hawking for minimal scalars. Some remarks about energy flow for SdS
BHs in regime of evaporation or anti-evaporation are also done. Study of no
boundary condition shows that this condition supports anti-evaporation for
nucleated BHs (at least in frames of our approximation). That indicates to the
possibility that some pair created cosmological BHs may not only evaporate but
also anti-evaporate. Hence, cosmological primordial BHs may survive much longer
than it is expected.
