  We investigate protostellar collapse of molecular cloud cores by numerical
simulations, taking into account turbulence and magnetic fields. By using the
adaptive mesh refinement technique, the collapse is followed over a wide
dynamic range from the scale of a turbulent cloud core to that of the first
core. The cloud core is lumpy in the low density region owing to the
turbulence, while it has a smooth density distribution in the dense region
produced by the collapse. The shape of the dense region depends mainly on the
mass of the cloud core; a massive cloud core tends to be prolate while a less
massive cloud core tends to be oblate. In both cases, anisotropy of the dense
region increases during the isothermal collapse. The minor axis of the dense
region is always oriented parallel to the local magnetic field. All the models
eventually yield spherical first cores supported mainly by the thermal
pressure. Most of turbulent cloud cores exhibit protostellar outflows around
the first cores. These outflows are classified into two types, bipolar and
spiral flows, according to the morphology of the associated magnetic field.
Bipolar flow often appears in the less massive cloud core. The rotation axis of
the first core is oriented parallel to the local magnetic field for bipolar
flow, while the orientation of the rotation axis from the global magnetic field
depends on the magnetic field strength. In spiral flow, the rotation axis is
not aligned with the local magnetic field.
