  According to General Relativity, astrophysical black holes are described by a
small number of parameters. Apart from the mass of the black hole (M), among
the most interesting characteristics is the spin (a), which determines the
degree of rotation, i.e., the angular momentum of the black hole. The latter is
observationally constrained by the spectral and timing properties of the
radiation signal emerging from an accretion disk of matter orbiting near the
event horizon. In the case of planar (standard, equatorial) accretion disk, it
is the location of the Innermost Stable Circular Orbit (ISCO) that determines
the observable radiation characteristics, and this way allows us to measure the
spin. In this paper, we discuss a more general case of the Innermost Stable
Spherical Orbits (ISSO) extending above and below the equatorial plane. To this
end, we study the non-equatorial geodesic motion of particles following
inclined, spherical, relativistically precessing trajectories with the aim of
exploring the boundary between the regions of stable (energetically bound) and
escaping (energetically unbound) motion. The concept of the ISSO radius should
play a role in determining the inner rim of a tilted or geometrically thick
accretion flow. We demonstrate that the region of inclined bound orbits has a
complicated structure due to enhanced precession near the inner rim. We also
explore the fate of particles launched below the radius of the Marginally Bound
Spherical Orbit (MBSO): these may either plunge into the event horizon or
escape to radial infinity.
