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In the 1980's, work by Coleman and by Giddings and Strominger linked thephysics of spacetime wormholes to `baby universes' and an ensemble of theories.We revisit such ideas, using features associated with a negative cosmologicalconstant and asymptotically AdS boundaries to strengthen the results, introducea change in perspective, and connect with recent replica wormhole discussionsof 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 bulkthat allow us to compute the full spectrum of associated boundary theories. Thedimension of the asymptotically AdS Hilbert space turns out to become a randomvariable $Z$, whose value can be less than the naive number $k$ of independentstates in the theory. For $k>Z$, consistency arises from an exact degeneracy inthe inner product defined by the gravitational path integral, so that many apriori independent states differ only by a null state. We argue that a similarproperty must hold in any consistent gravitational path integral. We alsocomment on other aspects of extrapolations to more complicated models, and onpossible implications for the black hole information problem in the individualmembers of the above ensemble.

Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information