Evolution of the slope of the fits of the KS relation from Figs. 2 and A.1, i.e., using the Bayesian fitting method, for the four mass bins considered, from the low-mass bin in a light color to the most massive one in a dark color. The red points show the slope of the entire galaxy population at a given redshift (i.e., without accounting for their mass, as in Fig. 3). After z ≈ 2 − 3, the slope of the KS relation for the two most massive bins remains within 30% (respectively 37%) of its final, converged, value for the molecular (respectively neutral) gas, which indicates the emergence of the KS relation at these redshifts. Low-mass galaxies do not show signs of convergence toward a fixed slope: their KS relation gets continuously shallower after z ≈ 2 − 3.