  Let N be a complete hyperbolic 3-manifold that is an algebraic limit of
geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the
interior of a compact 3-manifold, or tame, if one of the following conditions
holds:
  (1) N has non-empty conformal boundary,
  (2) N is not homotopy equivalent to a compression body, or
  (3) N is a strong limit of geometrically finite manifolds.
  The first case proves Ahlfors' measure conjecture for Kleinian groups in the
closure of the geometrically finite locus: given any algebraic limit G of
geometrically finite Kleinian groups, the limit set of G is either of Lebesgue
measure zero or all of the Riemann sphere. Thus, Ahlfors' conjecture is reduced
to the density conjecture of Bers, Sullivan, and Thurston.
