We investigate the time evolution of the angular momentum and induced toroidal magnetic field distribution in an initially nonrotating radiative stellar envelope containing a large scale poloidal magnetic field, following the impulsive spin-up of the underlying core. We present a large set of numerical calculations pertaining to monopolar, dipolar and quadrupolar magnetic configurations, with and without density gradients across the envelope, as well as a set of solutions for which the poloidal field is only partially anchored on the core. The use of the Galerkin finite element method yields an extremely robust computational scheme, allowing us to extend our calculations to higher Reynolds numbers (up to 10(5)) and longer time intervals (up to 10(4) Alfven times) than previously possible, without any hint of numerical misbehavior. The most striking feature of our fully core-anchored solutions is that a state of solid-body rotation is always attained, independent of poloidal field geometry or choice of Reynolds numbers. However, contrary to an often held belief, the time required to enforce a state of strict solid-body rotation (or very near solid-body rotation) is in general much longer than the core-surface Alfven transit time, and increases rather slowly with increasing Reynold numbers. Nevertheless, for field strengths of order 1 G, it still remains considerably shorter than main-sequence nuclear evolutionary time scales, and is one order of magnitude smaller than early main-sequence rotational evolution time scales. The relatively rapid transition toward solid-body rotation depends critically on all field lines having at least one footpoint anchored on the rigidly rotating core. This is unambiguously illustrated by our unanchored and partially anchored solutions, which in many cases either do not attain solid-body rotation, or do so on a purely viscous time scale. Clearly, a well-defined formulation of angular momentum transport by magnetic fields requires not only the specification of magnetic field strength and overall geometry, but also a detailed prescription of the field characteristics at the boundaries. Our computations also demonstrate that in moderate to high Reynolds number systems, any global magnetic dissipation time scale constructed using length scales of order of the stellar radius greatly overestimates the true dissipation time scale of the toroidal magnetic component. The relevant length scale is instead related to the wavelength of Alfvenic disturbances along field lines and to gradients in the toroidal magnetic field which develops across field lines. These gradients are the result of phase shifts induced by the path length differences accumulated by Alfven waves travelling along neighboring field lines. Not surprisingly, the true magnetic dissipation time scale associated with this phase-mixing mechanism then depends rather sensitively on poloidal field geometry and associated boundary conditions.
