<p>We examine the behavior of sequences of states in the large <i>N</i> limit of AdS/CFT duality in cases in which the bulk duals involve baby universes or black holes. Such sequences generally fail to converge as pure states. Under suitable conditions, such as diverging coarse-grained entropy, they can converge to mixed states for the large <i>N</i> algebra, as in the case of black holes. For Euclidean preparations that produce baby universes, the sequences do not converge, due to wormhole contributions, and so these states cannot admit large <i>N</i> limits. Nevertheless, appropriate averaging over <i>N</i> can lead to convergence to a mixed state. The associated algebras have nontrivial commutants, which can possibly be interpreted as operators in the baby universe.</p>