Total, central, and wandering BHOFs for the full population from z = 5 to z = 0. The total BHOF remains close to unity across the studied stellar mass and redshift ranges, indicating that most galaxies in the sample host at least one BH. However, the balance between central and wandering BHs evolves strongly: at low stellar masses, the central BHOF decreases toward z = 0, while the wandering BHOF increases. This demonstrates that late-time low-mass galaxies can remain occupied even when their BHs are displaced from the galaxy center. Gray bands show local observational constraints from Z25, with a solid line marking the median and shaded regions indicating the 1σ, 2σ, and 3σ intervals.