We prove that the Gromov–Hausdorff limit of Kähler–Ricci flow on a G-spherical Fano manifold X is a G-spherical $\mathbb{Q}$-Fano variety X_∞, which admits a (singular) Kähler–Ricci soliton. Moreover, the G-spherical variety structure of X_∞ can be constructed as a center of torus ${\mathbb{C}}^{\ast }$-degeneration of X induced by an element in the Lie algebra of Cartan torus of G.

We prove the following result: if a $\mathbb{Q}$-Fano variety is uniformly K-stable, then it admits a Kähler–Einstein metric. This proves the uniform version of Yau–Tian–Donaldson conjecture for all (singular) Fano varieties with discrete automorphism groups. We achieve this by modifying Berman–Boucksom–Jonsson's strategy in the smooth case with appropriate perturbative arguments. This perturbation approach depends on the valuative criterion and non-Archimedean estimates, and is motivated by our previous paper.