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We study the evolution of isothermal, rotating, magnetic, self-gravitating molecular clouds through numerical solution of the two-fluid MHD equations in axisymmetric geometry. The formation and contraction of cores (or fragments) is followed through both the quasistatic and dynamic phases of evolution, until the central density increases by six orders of magnitude. The evolution away from an initial equilibrium state is initiated entirely by magnetic braking (transport of angular momentum by torsional Alfv\'{e}n waves) and/or ambipolar diffusion (drift of neutrals relative to plasma). Typically, the mass in the central flux tubes initially increases on the ambipolar diffusion time scale, while magnetic braking enforces near corotation with the background medium. This phase continues until a magnetically and thermally supercritical core forms. Subsequently, the core evolves much more rapidly than its surroundings, creating a clear core-envelope separation. As far as rotation is concerned, the evolution of the central region occurs in three distinct phases: $(i)$ an exponential decrease of the angular velocity $\Omega_{\rm c}(t)$ due to effective magnetic braking, followed by $(ii)$ a constant $\Omega$ phase, which lasts until a supercritical core forms. Then $(iii)$ a constant angular momentum $(J)$ phase sets in.
A parameter study reveals that, by a central density enhancement of $10^{6}$ (e.g. from $3 \times 10^{3}$ to $3 \times 10^{9}$ cm$^{-3}$), masses of protostellar cores are in the range $\approx 1 - 30\, M_{\odot}$, and the corresponding specific angular momenta $(J/M)$ are in the range $\approx 10^{19} - 3 \times 10^{21}$ cm$^{2}$ s$^{-1}$, in agreement with protosolar-nebula and binary-star values.
