N_H vs. λ_Edd. We only compare sources with N_H derived from spectral analysis. We report as colored points the luminous QSOs and in gray Swift-BAT low-luminosity AGN (Ricci et al. 2017b). The filled and empty red stars represent W0410−09 for the BORUS and MYTORUS models, respectively. The hatched light blue region represents the range of N_H values derived from previous Hot DOG X-ray analyses (Assef et al. 2016; Vito et al. 2018; Zappacosta et al. 2018), and the λ_Edd range was determined using the BH masses estimated by Li et al. (2024, see our Sect. 5.2 for details). For hyperluminous optical QSOs, we show ±1σ range of λ_Edd values for the most luminous QSOs at z ≳ 2 in SDSS DR3 (downward-pointing light blue triangle marker, plotted at N_H = 10²¹ cm⁻²). The crosses show local (z ∼ 0.037) Swift-BAT AGN (Ricci et al. 2017b). The light gray zone represents the blow-out region for radiation trapping, where the radiation emitted by the black hole is trapped in the surrounding gas through a process of repeated absorption and reemission, causing continuous heating and accelerating the gas outward (Ishibashi et al. 2018). The white zone indicates the blow-out region in the single-scattering approximation. Below, the dot-dashed line separates nuclear from the host-scale absorption.