  We perform three-dimensional radiation non-ideal magnetohydrodynamics
simulations and investigate the impact of the Hall effect on the angular
momentum evolution in the collapsing cloud cores in which the magnetic field
$\magB$ and angular momentum $\angJ$ are misaligned with each other. We find
that the Hall effect notably changes the magnetic torques in the pseudo-disk,
and strengthens and weakens the magnetic braking in cores with an acute and
obtuse relative angles between $\magB$ and $\angJ$, respectively. This suggests
that the bimodal evolution of the disk size may occur in early disk
evolutionary phase even if $\magB$ and $\angJ$ are randomly distributed. We
show that a counter-rotating envelope form in the upper envelope of the
pseudo-disk in cloud cores with obtuse relative angles. We also find that a
counter-rotating region forms at the midplane of the pseudo-disk in cloud cores
with acute relative angles. The former and latter types of counter-rotating
envelopes may be associated with the YSOs with a large ($r\sim100$ AU) and
small ($r\lesssim10$ AU) disks, respectively.
