  We investigate the accretion induced spin up of the black hole via numerical
simulations. Our method is based on general-relativistic magneto-hydrodynamics
of the slowly-rotating flows in the Kerr metric, where possibly transonic shock
fronts may form. We account for the changing black hole mass and spin during
accretion which enforces dynamical evolution of the space-time metric. We first
study non-magnetized flows with shocks, and we also include magnetic field
endowed in the gas. The aim of this study is to verify whether the high mass
black holes may be produced with large spins, even though at birth the
collapsars might have contained slowly, or moderately spinning cores. In this
way, we put constraints on the content of angular momentum in the collapsing
massive stars. Our studies are also showing that shock fronts and magnetic
fields may halt accretion and limit the black hole spin-up in the exploding
supernovae.

High Energy Astrophysical Phenomena