  We consider formation of accretion disks from a realistically turbulent
molecular gas using 3D MHD simulations. In particular, we analyze the effect of
the fast turbulent reconnection described by the Lazarian & Vishniac (1999)
model for the removal of magnetic flux from a disk. With our numerical
simulations we demonstrate how the fast reconnection enables protostellar disk
formation resolving the so-called "magnetic braking catastrophe". In
particular, we provide a detailed study of the dynamics of a 0.5 M$_\odot$
protostar and the formation of its disk for up to several thousands years. We
measure the evolution of the mass, angular momentum, magnetic field, and
turbulence around the star. We consider effects of two processes that strongly
affect the magnetic transfer of angular momentum, both of which are based on
turbulent reconnection: the first, "reconnection diffusion", removes the
magnetic flux from the disk, the other involves the change of the magnetic
field's topology, but does not change the absolute value of the magnetic flux
through the disk. We demonstrate that for the first mechanism, turbulence
causes a magnetic flux transport outward from the inner disk to the ambient
medium, thus decreasing the coupling of the disk to the ambient material. A
similar effect is achieved through the change of the magnetic field's topology
from a split monopole configuration to a dipole configuration. We explore how
both mechanisms prevent the catastrophic loss of disk angular momentum and
compare both above turbulent reconnection mechanisms with alternative
mechanisms from the literature.
