Average distribution of the sum along the line of sight (x-axis) of the electron density (A), the parallel component of the magnetic field (B). the product of those two quantities (C), and the product divided by the (1 +z)⁻² contribution, for N_tree = 10³ MTs of our model with M_clust = 10¹⁵M_⊙. In the same panel, each distribution corresponds to a given redshift value. Each histogram is fitted with a skew-normal distribution (see Appendix C of Rappaz & Schober 2024) which is shown in solid lines and the median value of the latter is displayed in dotted lines, to highlight which parameter amongst the electron density and the line-of-sight component of the magnetic field has the most influence on the rotation measure. It appears that if the contribution of the expansion of the universe is not taken into account, the distribution of thermal electron density is dominant. With the expansion, the RM shows minor variations.