  We study the self-similar collapse of an isothermal magnetized rotating cloud
in the ideal magnetohydrodynamic (MHD) regime. In the limit of small distance
from the accreting protostar we find an analytic solution that corresponds to
free-fall onto a central mass point. The density distribution is not
spherically symmetric but depends on the mass loading of magnetic field lines,
which can be obtained by matching our inner solution to an outer collapse
solution previously computed by Allen, Shu & Li. The concentration of magnetic
field trapped by the central mass point under field-freezing, independent on
the details of the starting state, creates a split monopole configuration where
the magnetic field strength increases as the inverse square of the distance
from the center. Under such conditions, the inflow eventually becomes
subalfvenic and the outward transfer of angular momentum by magnetic braking
very efficient, thus preventing the formation of a centrifugally supported
disk. Instead, the azimuthal velocity of the infalling gas decreases to zero at
the center, and the gas spirals into the star. Therefore, the dissipation of
dynamically important levels of magnetic field is a fundamental requisite for
the formation of protoplanetary disks around young stars.
