  This is the third and final paper in a series which establish results
announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff
limits of metrics with cone singularities in the case when the limiting cone
angle approaches 2\pi. We also put all our technical results together to
complete the proof of the main theorem that if a K-stable Fano manifold admits
a Kahler-Einstein metric.
