HI (top) and H₂ (bottom) masses versus M_vir (left), M_star (centre), and SFR (right). Observational fits for HI and H₂ data are shown by grey dotted lines and MUSE-ALMA Haloes H₂ upper limits (Bollo et al. 2026) by grey circles and arrows. The fit to the MUSE-ALMA Haloes M_HI vs. M_star is Log(M_HI/M_⊙) = 0.50 Log(M_star/M_⊙)+4.52 (O’Beirne et al. 2026, priv. comm.) and is extrapolated from galaxy data at M_star ∼ 10⁸–10¹² M_⊙. Multi-parametric fits by Salvestrini et al. (2025) are shown for SFR = 10⁻¹ M_⊙ yr⁻¹ (lower central panel) and M_star = 10^8.5, 10⁷, and 10^5.5 M_⊙ (dotted lines from top to bottom in the lower right panel). Simulation fits (dashed magenta lines) are in Appendix F (Table F.2). Results are little dependent on redshift and feature a large environment-driven scatter.