The (log of the) gas-phase metallicity as a function of the black hole mass. Columns (left to right) show results PBH-seeded systems with spin = 0, –1 and +1, as marked; rows (from top to bottom) show results at z ∼ 5, 7 and 10. In each panel, colours show the associated stellar mass for each source from PHANES, as marked in panel c. Finally, the (filled) square at z ∼ 7 shows the (upper limits on the) metallicity estimate for Abell2744-QSO1 from Maiolino et al. (2025b); the (filled) circle at z ∼ 10 shows upper limits on the metallicity estimate of CANUCS-LRD-z8.6 at z ∼ 8.6 from Tripodi et al. (2024).