We use a 3-D relativistic SPH (Smoothed Particle Hydrodynamics) code to study
mergers of black hole -- neutron star (BH--NS) binary systems with low mass
ratios, adopting MNS/MBH≃0.1 as a representative case. The
outcome of such mergers depends sensitively on both the magnitude of the BH
spin and its obliquity (i.e., the inclination of the binary orbit with respect
to the equatorial plane of the BH). In particular, only systems with
sufficiently high BH spin parameter a and sufficiently low orbital
inclinations allow any NS matter to escape or to form a long-lived disk outside
the BH horizon after disruption. Mergers of binaries with orbital inclinations
above ∼60o lead to complete prompt accretion of the entire NS by the BH,
even for the case of an extreme Kerr BH. We find that the formation of a
significant disk or torus of NS material around the BH always requires a
near-maximal BH spin and a low initial inclination of the NS orbit just prior
to merger.Comment: to appear in ApJ, 54 pages, 19 figure