Distance from the galactic centre as a function of the host stellar mass at the last output (z = 4.41) for MBHs that have previously experienced a recoil kick, which includes wandering (orange triangles), escaping (red squares), and escaped (purple crosses) MBHs. We also show the distribution of MBHs that have not experienced a merger that are main (dark blue empty circles), satellite (blue empty circles), or halo (light blue empty circles) MBHs. See the text for details of the sample selection. The distance corresponding to 4Δx is denoted with a dashed line.