Space of ricci flows (II)- Part B: Weak compactness of the flows

Based on the compactness of the moduli of non-collapsed Calabi-Yau spaces with mild singularities, we set up a structure theory for polarized Kahler Ricci ows with proper geometric bounds. Our theory is a generalization of the structure theory of non-collapsed Kahler Einstein manifolds. As applications, we show the convergence of the Kahler Ricci ow in an appropriate topology and prove the partial-C'-conjecture.