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We follow the ambipolar-diffusion--driven formation and evolution of afragment in a magnetically supported molecular cloud, until a hydrostaticprotostellar core forms at its center. This problem was formulated in Paper I.We determine the density, velocity and magnetic field as functions of space andtime, and the contribution of ambipolar diffusion and Ohmic dissipation to theresolution of the magnetic flux problem of star formation. The issue of whetherthe magnetic field ever decouples from the (neutral) matter is also addressed.We also find that the electrons do not decouple from the field lines beforethermal ionization becomes important and recouples the magnetic field to theneutral matter. Ohmic dissipation becomes more effective than ambipolardiffusion as a flux reduction mechanism only at the highest densities (a fewtimes 10^12 particles per cubic cm). In the high-density central parts of thecore, the magnetic field acquires an almost spatially uniform structure, with avalue that, at the end of the calculation (number density ~ 5 times 10^14particles per cubic cm), is found to be in excellent agreement with meteoriticmeasurements of magnetic fields in the protosolar nebula. Outside thehydrostatic protostellar core, a concentration of magnetic flux (a "magneticwall") forms, which gives rise to a magnetic shock. This magnetic shock is theprecursor of the repeated shocks found by Tassis & Mouschovias (2005) whichcause spasmodic accretion onto the hydrostatic core at later times.Comment: 15 pages, 12 figures, emulateapj; accepted for publication in the  Astrophysical Journa

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment. II. Typical Axisymmetric Solution