  We investigate the formation of circumstellar disks and outflows subsequent
to the collapse of molecular cloud cores with the magnetic field and
turbulence. Numerical simulations are performed by using an adaptive mesh
refinement to follow the evolution up to $\sim 1000$~yr after the formation of
a protostar. In the simulations, circumstellar disks are formed around the
protostars; those in magnetized models are considerably smaller than those in
nonmagnetized models, but their size increases with time. The models with
stronger magnetic field tends to produce smaller disks. During evolution in the
magnetized models, the mass ratios of a disk to a protostar is approximately
constant at $\sim 1-10$\%. The circumstellar disks are aligned according to
their angular momentum, and the outflows accelerate along the magnetic field on
the $10-100$~au scale; this produces a disk that is misaligned with the
outflow. The outflows are classified into two types: a magneto-centrifugal wind
and a spiral flow. In the latter, because of the geometry, the axis of rotation
is misaligned with the magnetic field. The magnetic field has an internal
structure in the cloud cores, which also causes misalignment between the
outflows and the magnetic field on the scale of the cloud core. The
distribution of the angular momentum vectors in a core also has a non-monotonic
internal structure. This should create a time-dependent accretion of angular
momenta onto the circumstellar disk. Therefore, the circumstellar disks are
expected to change their orientation as well as their sizes in the long-term
evolutions.
