  Let M be a compact, hyperbolizable 3-manifold with nonempty incompressible
boundary and let AH(\pi_1(M)) denote the space of (conjugacy classes of)
discrete faithful representations of \pi_1(M) into PSL 2 (C). The components of
the interior MP(\pi_1(M)) of AH(\pi_1(M)) (as a subset of the appropriate
representation variety) are enumerated by the space A(M) of marked
homeomorphism types of oriented, compact, irreducible 3-manifolds homotopy
equivalent to M. In this paper, we give a topological enumeration of the
components of the closure of MP(\pi_1(M)) and hence a conjectural topological
enumeration of the components of AH(\pi_1(M)). We do so by characterizing
exactly which changes of marked homeomorphism type can occur in the algebraic
limit of a sequence of isomorphic freely indecomposable Kleinian groups. We use
this enumeration to exhibit manifolds M for which AH(\pi_1(M)) has infinitely
many components.
