  There is observational evidence that the X-ray continuum source that creates
the broad fluorescent emission lines in some Seyfert Galaxies may be compact
and located at a few gravitational radii above the black hole. We consider the
possibility that this compact source may be powered by small scale flux tubes
near the black hole that are attached to the orbiting accretion disk. As a
first step, this paper investigates the salient features of black hole
magnetospheres that contain small scale, disk-hole linking "closed" flux tubes,
using the force-free approximation in an axisymmetric setting. We find that the
extent of the closed zone is a result of the balance between the black hole
spin induced twist in the closed zone and the confinement pressure of the
external (open) field of the disk. The maximal extent of the closed zone, for a
typical external confinement, is usually a few gravitational radii. The
pressure competition between the closed zone and the external confinement could
in principle lead to interesting dynamics and dissipation relevant for the
compact X-ray corona.
