Iso-contours of the conditional density distribution of the halo sparsity, ρ(s_200,500|M_200,c). Measurements are from the Uchuu halo catalogue at z = 0, (top panel), estimated from the distribution of measured concentrations (central panel), and predicted assuming a log-normal distribution of the concentration parameter for which the mean is given by the c − M relation of Ishiyama et al. (2021) calibrated on the Uchuu catalogues and width paramter σ = 0.25 (bottom panel). The coloured lines correspond to the mean of the distribution of measured sparsities (red), and that inferred from the measured concentrations (orange) and from the log-normal distribution (yellow).