  We employ the first fully three-dimensional simulation to study the role of
magnetic fields and ion-neutral friction in regulating gravitationally-driven
fragmentation of molecular clouds. The cores in an initially subcritical cloud
develop gradually over an ambipolar diffusion time while the cores in an
initially supercritical cloud develop in a dynamical time. The infall speeds on
to cores are subsonic in the case of an initially subcritical cloud, while an
extended (\ga 0.1 pc) region of supersonic infall exists in the case of an
initially supercritical cloud. These results are consistent with previous
two-dimensional simulations. We also found that a snapshot of the relation
between density (rho) and the strength of the magnetic field (B) at different
spatial points of the cloud coincides with the evolutionary track of an
individual core. When the density becomes large, both relations tend to B
\propto \rho^{0.5}.
