Average black hole mass accretion histories as predicted from DECODE, compared to those predicted from Zou et al. (2024a, dash-dotted lines). DECODE’s results are shown both for the accretion-only scenario (solid lines) and the scenario with mergers (dotted lines). The filled circles and triangles show the redshift at which half of the black hole mass is formed. The different colours show the accretion tracks for different black mass bins at z = 0: log₁₀(M_BH/M_⊙)≃6.75 (blue lines), log₁₀(M_BH/M_⊙)≃7.25 (orange lines), log₁₀(M_BH/M_⊙)≃7.75 (green lines), log₁₀(M_BH/M_⊙)≃8.2 (red lines), and log₁₀(M_BH/M_⊙)≃8.6 (purple lines).