Left panel: Stellar halo mass as a function of the transition radius R_trans at different redshifts, as indicated in the legend. The two dashed black lines represent the 16th and 84th percentiles of the distribution at z = 0. Right panel: Distribution of transition radii at different redshifts (different colors) and as inferred from observations (VEGAS, green line). The model distributions extend to systematically higher values of R_trans than the observational one, while the VEGAS distribution is more narrowly peaked at smaller radii (see the vertical lines indicating medians, 16th and 84th percentiles of the distributions for the model predictions at z = 0 (black) and VEGAS (green)). This offset reflects the different definitions adopted in the SAM and in observations, as well as differences in sample selection. The comparison should therefore be interpreted in a statistical sense, focusing on typical scales and trends rather than on a one-to-one correspondence. Across all redshifts, the majority of model transition radii lie within ∼100 kpc, with a tail extending to higher values in the most massive systems.