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In two previous papers we formulated and solved, for a fiducial set of freeparameters, the problem of the formation and evolution of a magneticallysupercritical core inside a magnetically subcritical parent cloud. In thispaper we present a parameter study to assess the sensitivity of the results (1)to the density at which the equation of state becomes adiabatic; (2) to theinitial mass-to-flux ratio of the parent cloud; and (3) to ionization byradioactive decay of different nuclei (40K and 26Al) at high densities (numberdensity > 10^12 particles per cubic cm). We find that (1) the results dependonly slightly on the density at which the onset of adiabaticity occurs; (2)memory of the initial mass-to-flux ratio is completely lost at late times,which emphasizes the relevance of this work, idependently of the adopted theoryof core formation; and (3) the precise source of radioactive ionization altersthe degree of attachment of the electrons to the field lines (at highdensities), and the relative importance of ambipolar diffusion and Ohmicdissipation in reducing the magnetic flux of the protostar. The value of themagnetic field at the end of the runs is insensitive to the values of the freeparameters and in excellent agreement with meteoritic measurements of theprotosolar nebula magnetic field. The magnetic flux problem of star formationis resolved for at least strongly magnetic newborn stars. A complete detachmentof the magnetic field from the matter is unlikely. The formation of a "magneticwall" (with an associated magnetic shock) is independent of the assumedequation of state, although the process is enhanced and accelerated by theformation of a central hydrostatic core.Comment: 17 pages, 14 figures, emulateapj; accepted for publication in the  Astrophysical Journa

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment. III. A Parameter Study