Upper panels: Quasar luminosity function at z  =  0.5, 2, 3, 5, 6, and 7 predicted by the Fiducial (blue) and Off-center (orange) models. The results of L-GalaxiesBH are presented for the Millennium trees with the grafting methodology. Shaded areas show the Poisson error. Observational data correspond to Shen et al. (2020), Lacy et al. (2015), Kokorev et al. (2024), Greene et al. (2024), Matthee et al. (2024), Akins et al. (2025), and Barlow-Hall & Aird (2025). Lower panels: Ratio between the predictions of the Off-center and Fiducial models. The horizontal grey lines are placed at 0.5, 1, 2, and 5 to guide the eye. Upper panels: Quasar luminosity function at z  =  0.5, 2, 3, 5, 6, and 7 predicted by the Fiducial (blue) and Off-center (orange) models. The results of L-GalaxiesBH are presented for the Millennium trees with the grafting methodology. Shaded areas show the Poisson error. Observational data correspond to Shen et al. (2020), Lacy et al. (2015), Kokorev et al. (2024), Greene et al. (2024), Matthee et al. (2024), Akins et al. (2025), and Barlow-Hall & Aird (2025). Lower panels: Ratio between the predictions of the Off-center and Fiducial models. The horizontal grey lines are placed at 0.5, 1, 2, and 5 to guide the eye.