  In this paper we analyze the long-time behavior of 3 dimensional Ricci flows
with surgery. Our main result is that if the surgeries are performed correctly,
then only finitely many surgeries occur and after some time the curvature is
bounded by $C t^{-1}$. This result confirms a conjecture of Perelman. In the
course of the proof, we also obtain a qualitative description of the geometry
as $t \to \infty$.
  This paper is the third part of a series. Previously, we had to impose a
certain topological condition $\mathcal{T}_2$ to establish the finiteness of
the surgeries and the curvature control. The objective of this paper is to
remove this condition and to generalize the result to arbitrary closed
3-manifolds. This goal is achieved by a new area evolution estimate for minimal
simplicial complexes, which is of independent interest.
