Cumulative number of wandering BHs to the total number of BHs found in the D9 region as a function of the BH mass at z = 0 (left panel), and as a function of redshift for z = 3, z = 1, and z = 0 (right panel). In the left panel, no mass threshold is adopted to select the BHs, and hence all the BHs with mass above the seeding mass are included (see Table 2). In both panels, the simulation using the DF model, marked with a blue line, is compared with REPOS in red and DYNMASS in green. The wandering BHs are defined as those having a distance larger than two times the R_HMS from the closest sub-halo.