  If the angular momentum of the molecular cloud core were conserved during the
star formation process, a new-born star would rotate much faster than its
fission speed. This constitutes the angular momentum problem of new-born stars.
In this paper, the angular momentum transfer in the contraction of a rotating
magnetized cloud is studied with axisymmetric MHD simulations. Owing to the
large dynamic range covered by the nested-grid method, the structure of the
cloud in the range from 10 AU to 0.1 pc is explored. First, the cloud
experiences a run-away collapse, and a disk forms perpendicularly to the
magnetic field, in which the central density increases greatly in a finite
time-scale. In this phase, the specific angular momentum j of the disk
decreases to $\simeq 1/3$ of the initial cloud. After the central density of
the disk exceeds $\sim 10^{10}{\rm cm}^{-3}$, the infall on to the central
object develops. In this accretion stage, the rotation motion and thus the
toroidal magnetic field drive the outflow. The angular momentum of the central
object is transferred efficiently by the outflow as well as the effect of the
magnetic stress. In 7000 yr from the core formation, the specific angular
momentum of the central $0.17M_\odot$ decreases a factor of 10^{-4} from the
initial value (i.e. from $10^{20}{\rm cm^2 s^{-1}}$ to $10^{16}{\rm cm^2
s^{-1}}$).
