  We study the Ricci flow on complete Kaehler metrics that live on the
complement of a divisor in a compact complex manifold. In earlier work, we
considered finite-volume metrics which, at spatial infinity, are transversely
hyperbolic. In the present paper we consider three different types of spatial
asymptotics: cylindrical, bulging and conical. We show that in each case, the
asymptotics are preserved by the Kaehler-Ricci flow. We address long-time
existence, parabolic blowdown limits and the role of the Kaehler-Ricci flow on
the divisor.
