Abstract: (Joint with Chi Li) Inspired by the study of Sasakian-Einstein metric, fora a general Kawamata log terminal singularity, Chi Li has proposed an approach to give an algebraic process of degenerate the singularity to the semistable tangent cone, and then the polystable tangent cone. When the singularity is quasi-regular, we apply the construction of Koll\'ar components in minimal model program to investigate the question, and obtain applications in both the MMP side and the stability side.