Evolution of the MBH mass in the MAD (shown as a solid orange line) and HMAD (shown as a dashed blue line) simulations relative to the galaxy stellar mass compared with the local AGN observations by Reines & Volonteri (2015, grey dots), local ellipticals by Kormendy & Ho (2013, grey stars), and high-redshift (z ≳ 6) observations by ALMA (Neeleman et al. 2021, green squares) and JWST (Yue et al. 2024; Stone et al. 2023, 2024; Harikane et al. 2023; Maiolino et al. 2023, red diamonds). We also show the “little red dots” reported by Greene et al. (2024) as magenta crosses, with the stellar masses estimated with or without ALMA photometry, respectively, connected by magenta shaded areas (see Labbe et al. 2023, for details), and the z ∼ 10 MBH GN-z11 (Maiolino et al. 2024), thought to be super-Eddington, as a cyan hexagon. For completeness, we also show the results of the simulation in L19 as a dot-dashed black line.