In the 1980's, work by Coleman and by Giddings and Strominger linked the
physics of spacetime wormholes to `baby universes' and an ensemble of theories.
We revisit such ideas, using features associated with a negative cosmological
constant and asymptotically AdS boundaries to strengthen the results, introduce
a change in perspective, and connect with recent replica wormhole discussions
of the Page curve. A key new feature is an emphasis on the role of null states.
We explore this structure in detail in simple topological models of the bulk
that allow us to compute the full spectrum of associated boundary theories. The
dimension of the asymptotically AdS Hilbert space turns out to become a random
variable Z, whose value can be less than the naive number k of independent
states in the theory. For k>Z, consistency arises from an exact degeneracy in
the inner product defined by the gravitational path integral, so that many a
priori independent states differ only by a null state. We argue that a similar
property must hold in any consistent gravitational path integral. We also
comment on other aspects of extrapolations to more complicated models, and on
possible implications for the black hole information problem in the individual
members of the above ensemble
