  Black hole (BH) accretion flows and jets are qualitatively affected by the
presence of ordered magnetic fields. We study fully three-dimensional global
general relativistic magnetohydrodynamic (MHD) simulations of radially extended
and thick (height $H$ to cylindrical radius $R$ ratio of $|H/R|\sim 0.2--1$)
accretion flows around BHs with various dimensionless spins ($a/M$, with BH
mass $M$) and with initially toroidally-dominated ($\phi$-directed) and
poloidally-dominated ($R-z$ directed) magnetic fields. Firstly, for toroidal
field models and BHs with high enough $|a/M|$, coherent large-scale (i.e. $\gg
H$) dipolar poloidal magnetic flux patches emerge, thread the BH, and generate
transient relativistic jets. Secondly, for poloidal field models, poloidal
magnetic flux readily accretes through the disk from large radii and builds-up
to a natural saturation point near the BH. For sufficiently high $|a/M|$ or low
$|H/R|$ the polar magnetic field compresses the inflow into a geometrically
thin highly non-axisymmetric "magnetically choked accretion flow" (MCAF) within
which the standard linear magneto-rotational instability is suppressed. The
condition of a highly-magnetized state over most of the horizon is optimal for
the Blandford-Znajek mechanism that generates persistent relativistic jets with
$\gtrsim 100$% efficiency for $|a/M|\gtrsim 0.9$. A magnetic Rayleigh-Taylor
and Kelvin-Helmholtz unstable magnetospheric interface forms between the
compressed inflow and bulging jet magnetosphere, which drives a new jet-disk
quasi-periodic oscillation (JD-QPO) mechanism. The high-frequency QPO has
spherical harmonic $|m|=1$ mode period of $\tau\sim 70GM/c^3$ for $a/M\sim 0.9$
with coherence quality factors $Q\gtrsim 10$. [abridged]
