  We report on key studies on the dynamics of black holes (BHs) in gas-rich
galaxy mergers that underscore the vital role played by gas dissipation in
promoting BH inspiral down to the smallest scales ever probed with use of
high-resolution numerical simulations. In major mergers, the BHs sink rapidly
under the action of gas-dynamical friction while orbiting inside the massive
nuclear disc resulting from the merger. The BHs then bind and form a Keplerian
binary on a scale of 5 pc. In minor mergers, BH pairing proceeds down to the
minimum scale explored of 10-100 pc only when the gas fraction in the less
massive galaxy is comparatively large to avoid its tidal and/or ram pressure
disruption and the wandering of the light BH in the periphery of the main halo.
Binary BHs enter the gravitational wave dominated inspiral only when their
relative distance is typically of 0.001 pc. If the gas preserves the degree of
dissipation expected in a star-burst environment, binary decay continues down
to 0.1 pc, the smallest length-scale ever attained. Stalling versus hardening
below 0.1 pc is still matter of deep investigations.
