Upper panel: best-fit nanohertz GW signals found using the BH mass-stellar mass relations proposed in Pacucci & Loeb (2024), Li et al. (2024), and our global fit (3) compared to the signal measured by NANOGrav (grey). We imposed α = 8/3, as expected from gas infall (see the discussion below Eq. (12)). Lower panel: chirp masses and red-shifts of 100 realisations of the strongest binary contributing to the first bin of the upper panel for the scenarios proposed in Pacucci & Loeb (2024), and Li et al. (2024) compared with our analysis (Ellis et al. 2024a). Contours of log₁₀Ω_GW are shown for comparison.