  This paper is a continuation of I, (same title), and is concerned with the
existence, regularity and degeneration of metrics minimizing natural curvature
functionals on the space of metrics on 3-manifolds. The functionals chosen are
designed to be optimal w.r.t. the issue of geometrization of the underlying
3-manifold, in the sense of Thurston. Two of the main results are Theorems B
and C, in comparison with Theorem A of I.
