Two examples of the interaction between the central BH and stellar sub-structures. In (A, top row), when the background spherical Isochrone potential is partially frozen, the disc stars form clumps of higher mass and binding energy. Such structures may dislodge the BH. This two-stage instability then grows as the BH extracts angular momentum from the flow of rotating stars around the centre. In (B, bottom row) the situation for a self-gravitating disc plus isochrone potential means that the clumps are much less massive and of a lower binding energy. In that case, a clump will dissolve in the strong tidal field of the BH. The centre of coordinates is indicated with a red dot. (See text for more details).