Dynamical collapse of rotating cloud and subsequent mass supply to the central object is the basic physical process on the formation of the central black holes in the high-z QSO cosmologically. Considering the formation of super massive black holes, the centrifugal barrier plays an important role. In this contribution, I consider the viscous effect to the self-gravitating disk which formed cosmologically. In particular, unsteady growth of the central core is treated consistently with surrounding accreting disks semi-analytically. A new self-similar solution of axisymmetric viscous accretion onto an evolving point mass is obtained. Application to QSO progenitor black hole formation is briefly discussed.