A large variety of spacetimes - including the BTZ black holes - can be obtained by identifying points in (2 + 1)-dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained under a restriction to time-symmetric initial data and one asymptotic region only. The resulting spacetimes are non-eternal black holes with collapsing wormhole topologies. Our approach is geometrical, and we discuss in detail the allowed topologies, the shape of the event horizons, topological censorship and trapped curves.
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