  In paper I, we showed that time-dependent general relativistic
magnetohydrodynamic (GRMHD) numerical models of accretion disks, although being
highly turbulent, have surprisingly simple electromagnetic properties. In
particular, the toroidal current density in the disk takes the form $dI_\phi/dr
\propto r^{-5/4}$. Guided by this simplicity, we use a time-dependent general
relativistic force-free electrodynamics (GRFFE) code to study an idealized
problem in which the accretion disk is replaced by an infinitely thin rotating
equatorial current sheet. We consider both an $r^{-5/4}$ current profile and an
$r^{-1}$ profile, the latter corresponding to the paraboloidal model of
Blandford & Znajek (1977). The force-free magnetosphere we obtain with the
$r^{-5/4}$ current sheet matches remarkably well to the Poynting-dominated jet
seen in GRMHD numerical models. By comparing to the non-rotating force-free
model studied in paper I, rotation is seen to lead to mild decollimation of the
jet suggesting that hoop-stress forces nearly cancel centrifugal forces. In
order to study the process that generates the corona and disk wind and destroys
the ordered field in the corona in GRMHD numerical models, the force-free field
with the $r^{-5/4}$ current distribution is embedded in an accretion disk and
followed in a GRMHD simulation. Reconnection and magnetic stresses contribute
to a magnetized, thermal wind without the aid of an ordered field threading the
disk.
