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.
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