Are a black hole's jets caused by the black hole's magnetic field? Do the jets sometimes emitted by a black hole result from its magnetic field?  It would seem Jupiter's magnetic field tends to be concentrated at the poles, and I would imagine this might extend to black holes as well.  I could see the concentrated fields near the poles accelerating particles either into or away from the black hole at high speeds.  I have included an image of Jupiter's magnetic field below:

http://en.wikipedia.org/wiki/Magnetosphere_of_Jupiter#Role_of_Io



It also appears that a black hole's magnetic field is indeed very strong:
http://www.iflscience.com/space/magnetic-fields-can-be-strong-black-holes-gravity
You appear to have a thing about linking the magnetic field generated by Jupiter to that around a black hole (note that a field does not "belong" to an object) - the two things are entirely different, the only connection being that magnetic fields are generated in both cases by currents caused by the motion of charged particles.

In Jupiter's case, the magnetic field is (likely) generated via a dynamo process, involving currents that flow in its metallic hydrogen interior.

In the case of a black hole, as material travels inwards, it forms an accretion disk around the black hole (because angular momentum must be conserved), in which magnetic field can be generated and amplified. The twisting of the magnetic field lines around the rotation axis of the black hole could create a kind of magnetic funnel lined up with the rotation axis, along which charged particles can be accelerated by a strong magnetic field gradient. The field lines would not look like you have shown for Jupiter, they would be twisted into a helical topology along the rotation axis. This is part of the Blandford-Znajek effect, which I do not claim to properly understand.

So the answer to your question is maybe, but its very much a topic of contemporary research.