Fractions of LISA MBHB sources (left panels) and single MBHs (right panels) hosted in elliptical (red), classical bulge (green), pseudobulge (blue), and extreme-late type (purple) galaxies at different redshifts. Top, middle, and bottom panels correspond to different mass bins: 10⁴ − 10⁵ M_⊙, 10⁵ − 10⁶ M_⊙, and 10⁶ − 10⁷ M_⊙, respectively. We note that the MBHB hosts have noisier distributions because their number density is up to 2 − 3 orders of magnitude smaller than that of single MBHs (see Fig. 5). Briefly, galaxies hosting LISA systems display a disc-dominated morphology whose bulge component is more pronounced towards lower redshifts.