Molecular gas mass as a function of the total (unobscured plus obscured) star-formation rate of our galaxies, colour-coded by redshift. The filled circles correspond to M_molgas determined with ${\alpha }_{\mathrm{CO}}^{\mathrm{SB}}=1M_{\odot }{(\mathrm{K}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{pc}}^2)}^{-1}$, and the dotted red segments show the range of possible M_molgas with higher CO-to-H₂ conversion factors up to ${\alpha }_{\mathrm{CO}}^{\mathrm{MW}}=4.36M_{\odot }{(\mathrm{K}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{pc}}^2)}^{-1}$. Whatever α_CO, our extreme starburst galaxies have significantly higher SFR_UV+IR than MS galaxies at comparable M_molgas (see the solid line as derived by Sargent et al. 2014). For ${\alpha }_{\mathrm{CO}}^{\mathrm{SB}}$ our galaxies are the first galaxies known at high redshift to reach the starburst M_molgas–SFR relation (dashed line) offset by > 1 dex from the MS relation, according to the parametrisation of Sargent et al. (2014) based on nearby and z < 0.1 ULIRGs.