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The constraints on star formation in and near a galactic nucleus are outlined, and the degree of the concentration of massive stellar remnants toward the nucleus is assessed. Within 10-100 parsecs of a galactic nucleus, star formation is strongly affected by the physical extremes of the nuclear region: strong tidal forces, strongly enhanced cloud turbulence and gas heating, and relatively large magnetic fields. Black hole remnants of massive stars will inevitably migrate in the central stellar core of a galaxy and be concentrated there. The radius from which they will sink into the core in the galaxy's lifetime depends on the central mass concentration; for the Milky Way, it is about 4 pc. Close gravitational interactions of stellar remnants with red giants in the central stellar core of the Galaxy occur with sufficient frequency to be important for the evolution of both. The stellar core of the Galaxy is currently bereft of gas, except for the winds emanating from the luminous stellar objects located there.
M. Morris (Sat,) studied this question.