Distribution of azimuthal symmetric excess, β (as defined in Eq. (12)), computed inside clusters (R <  R₂₀₀) in top panels and at cluster peripheries (1 <  R[R₂₀₀]< 2) in bottom panels, as a function of different halo properties: level of relaxation on the left, mass-accretion rate in the middle, and formation redshift on the right. The mean profiles of β and their errors are shown in solid lines. The number of objects used to compute the average in each bin of the x-axis (shown with grey dotted lines) is written above the figures in grey.