Stellar density projection along the z-axis with depths of 100 kpc (top) and 300 kpc (bottom), centred on the position of a wandering BH at redshiſt z = 3 (tagged as BH 2; left panel), and of a wandering BH at z = 0.06 (tagged as BH 4; right panel) in the D9 simulation using the REPOS scheme. In both panels, the cyan crosses identify the wandering BHs, while the green crosses identify the BHs centred in their host. We show sub-halo centres as white shaded dots, with the white circles indicating the corresponding R_HMS. On the top and on the right of each panel we show the gravitational potential Φ of all the star particles (light white dots) and of the BHs (crosses) in the field, projected along the two orthogonal directions.