  The outflow efficiency (eta) from black hole (BH) accretion disc systems is
known to depend upon both the BH spin (a) and the amount of large-scale
magnetic flux threading the BH and disc. Semi-analytical flux-trapping models
suggest retrograde BHs should trap much more large-scale magnetic flux near the
BH leading to much higher eta than for prograde BHs. We self-consistently
determine the amount of large-scale magnetic flux trapped by rapidly spinning
(a = -0.9 and 0.9) BHs using global 3D time-dependent non-radiative general
relativistic magnetohydrodynamic simulations of thick (h/r ~ 0.3-0.6) discs. We
find that BH-trapped flux builds up until it is strong enough to disrupt the
inner accretion disc. Contrary to prior flux-trapping models, which do not
include the back-reaction of magnetic flux on the disc, our simulations show
prograde BHs trap more magnetic flux, leading to about 3 times higher eta than
retrograde BHs for |a| = 0.9. Both spin orientations can produce highly
efficient jets, eta ~ 100%, with increasing eta for increasing disc thickness.
The similarity of eta for prograde and retrograde BHs makes it challenging to
infer the sign of BH spin based on jet energetics alone.
