  We investigate the evaporation process of a Kerr-de Sitter black hole with
the Unruh-Hawking-like vacuum state, which is a realistic vacuum state
modelling the evaporation process of a black hole originating from
gravitational collapse. We also compute the greybody factors for gravitons,
photons, and conformal-coupling massless scalar particles by using the analytic
solutions of the Teukolsky equation in the Kerr-de Sitter background. It turns
out that the cosmological constant quenches the amplification factor and it
approaches to zero towards the critical point where the Nariai and extremal
limits merge together. We confirm that even near the critical point, the
superradiance of gravitons is more significant than that of photons and scalar
particles. Angular momentum is carried out by particles several times faster
than mass energy decreases. This means that a Kerr-de Sitter black hole rapidly
spins down to a nearly Schwarzschild-de Sitter black hole before it completely
evaporates. We also compute the time evolution of the Bekenstein-Hawking
entropy. The total entropy of the Kerr-de Sitter black hole and cosmological
horizon increases with time, which is consistent with the generalized second
law of thermodynamics.
