Total, central, and wandering BHOFs from z = 5 to z = 0 for heavy-seed BHs (thick lines, left column) and active BHs (thick lines, right column). We define heavy-seed BHs as BHs for which the initial seed mass, or the seed mass of any progenitor that merged into them, exceeded 10⁵ M_⊙. We define active BHs as those with f_Edd > 0.01. Thin dotted lines mark the corresponding full-population BHOFs, while gray bands show local observational constraints from Z25. The heavy-seed BHOFs are substantially lower than the full-population BHOFs at low stellar masses, demonstrating that the low-mass end of the BHOF is sensitive to the underlying seed mass distribution. For active BHs, the total and central BHOFs decline strongly toward low redshift, particularly after cosmic noon, while the wandering BHOF is negligible at nearly all masses and redshifts. This shows that AGN-selected samples trace the accretion duty cycle rather than the intrinsic BHOF.