  We evaluate the tunneling and Hartle-Hawking wave functions on S^1 x S^2
boundaries in Einstein gravity with a positive cosmological constant. In the
large overall volume limit the classical predictions of both wave functions
include an ensemble of Schwarzschild-de Sitter black holes. We show that the
Hartle-Hawking tree level measure on the classical ensemble converges in the
small S^1 limit. A divergence in this regime can be identified in the tunneling
state. However we trace this to the contribution of an unphysical branch of
saddle points associated with negative mass black holes. Using a representation
in which all saddle points have an interior Euclidean anti-de Sitter region we
also generalise the holographic formulation of the semiclassical Hartle-Hawking
wave function to S^1 x S^2 boundaries.
