Horosymmetric limits of Kähler-Ricci flow on Fano $G$-manifolds

In this paper, we prove that on a Fano $\mathbf{G}$-manifold $(M,J)$, the Gromov-Hausdorff limit of Kähler-Ricci flow with initial metric in $2\pi c_1(M)$ must be a $\mathbb{Q}$-Fano horosymmetric variety $M_{\mathrm{\infty }}$, which admits a singular Kähler-Ricci soliton. Moreover, $M_{\mathrm{\infty }}$ is a limit of ${\mathbb{C}}^{\ast }$-degeneration of $M$ induced by an element in the Lie algebra of Cartan torus of $\mathbf{G}$. A similar result can be also proved for Kähler-Ricci flows on any Fano horosymmetric manifolds. As an application, we generalize our previous result about the type II singularity of Kähler-Ricci flows on Fano $\mathbf{G}$-manifolds to Fano horosymmetric manifolds.