Run0 velocities evolution. Left: evolution of the BH relative velocity (blue), the gas effective velocity (red, excluding a sphere of radius 5 pc around the BH), and sound speed (yellow) over time for Run0. Right: evolution of the BH relative velocity with superimposed fits to its time evolution. The dashed vertical lines in both panels mark the three phases of the BH deceleration. In the first phase the BHL radius is not well resolved, in the second the BHL radius is well resolved and deceleration is stronger, in the third the BH is in the transonic regime and does not decelerate further.