Redshift evolution of the maximum H₂ fractions reached in simulations without (solid black line; HM-HISSmed reference run) and with H₂ dust grain catalysis for T_gr= 75 K (purple short-dashed line; HM-HISS-cat-75-Zevol), 40 K (magenta dot-dot-dot-dashed line; HM-HISS-cat-40-Zevol), 120 K (blue dotted line; HM-HISS-cat-120-Zevol), T_gr(z)=T_CMB(z) (green dot-dashed line; HM-HISS-cat-Tcmb-Zevol) and T_gr(z)=T_β(z) with dust emissivity index β = 2 (red long dashed line; HM-HISS-cat-Tbeta-Zevol) are also considered. All the runs include metal spreading from stellar evolution, as indicated in the bottom right corner by Z(t).