Stellar density map along the z-axis with depth of 10 kpc in the top and central row and 70 kpc in the bottom row, centred on the central BH (BH_cen) of Event 1 in the top row, Event 2 in the central row and Event 3 in the bottom row. The maps of stellar density refer to the redshift indicated on the left panel of each row. In each panel, the curve show the orbit of the satellite BH (BH_sat) involved in the merger event, colour-coded according to the redshift. The crosses indicate the last position of the satellite BH before either the merging event or the end of the simulations (see Sect. 6). The columns display the BH evolution using different sub-resolution prescriptions, from the left: using DF (first column), using a boosted dynamical mass (second), adopting the repositioning scheme (third) and finally without any correction for BH dynamics (fourth).