Examples of evolutionary pathways for overmassive and undermassive MBHs. The upper panels show the galaxy merger trees, the middle panels illustrate the assembly of stellar mass and MBH mass, and the lower panels present the evolution of the ratio M_BH/M_*. The first column corresponds to an overmassive MBH whose growth is driven by the gradual stripping of the host galaxy. The second column shows an undermassive MBH produced by a GW recoil event. The third column depicts an undermassive MBH resulting from a quiescent merger history, while the fourth column presents an overmassive MBH formed through an active merger history combined with a super-Eddington accretion episode.