  We have carried out 2D and 3D general relativistic magnetohydrodynamic
simulations of jets launched self-consistently from accretion disks orbiting
Kerr black holes and applied the results to the inner engine of the collapsar
model of gamma-ray bursts. The accretion flow launches energetic jets in the
axial funnel region of the disk/jet system, as well as a substantial coronal
wind. The jets feature knot-like structures of extremely hot,
ultra-relativistic gas; the gas in these knots begins at moderate velocities
near the inner engine, and is accelerated to ultra-relativistic velocities
(Lorentz factors of 50, and higher) by the Lorentz force in the axial funnel.
The increase in jet velocity takes place in an acceleration zone extending to
at least a few hundred gravitational radii from the inner engine. The overall
energetics of the jets are strongly spin-dependent, with high-spin black holes
producing the highest energy and mass fluxes. In addition, with high-spin black
holes, the ultra-relativistic outflow is cylindrically collimated within a few
hundred gravitational radii of the black hole, whereas in the zero- spin case
the jet retains a constant opening angle of approximately 16 degrees. The
simulations also show that the coronal wind, though considerably slower and
colder than the jets, also carries a significant amount of mass and energy.
When simulation data is scaled to the physical dimensions of a collapsar the
jets operate for a period ranging from 0.1 to 1.4 seconds, until the accretion
disk is depleted, delivering $10^{48}$ to $10^{49}$ erg.
