  General relativistic numerical simulations of magnetized accretion flows
around black holes show a disordered electromagnetic structure in the disk and
corona and a highly relativistic, Poynting-dominated funnel jet in the polar
regions. The polar jet is nearly consistent with the stationary paraboloidal
Blandford-Znajek model of an organized field threading the polar regions of a
rotating black hole. How can a disordered accretion disk and corona lead to an
ordered jet? We show that the polar jet is associated with a strikingly simple
angular-integrated toroidal current distribution $dI_\phi/dr \propto r^{-5/4}$,
where $I_\phi(r)$ is the toroidal current enclosed inside radius $r$. We
demonstrate that the poloidal magnetic field in the simulated jet agrees well
with the force-free field solution for a non-rotating thin disk with an
$r^{-5/4}$ toroidal current, suggesting rotation leads to negligible
self-collimation. We find that the polar field is confined/collimated by the
corona. The electromagnetic field in the disk also scales as $r^{-5/4}$, which
is consistent with some Newtonian accretion models that assume rough
equipartition between magnetic and gas pressure. However, the agreement is
accidental since toward the black hole the magnetic pressure increases faster
than the gas pressure. This field dominance near the black hole is associated
with magnetic stresses that imply a large effective viscosity parameter
$\alpha\sim 1$, whereas the typically assumed value of $\alpha\sim 0.1$ holds
far from the black hole.[abridged]
