Scale-lengths of the inner (h_i, top row) andouter profiles (h_o, middle row) and the ratio h_o/h_i (bottom row) as a function of the stellar mass. Left column: distribution of h_i, h_o and h_o /h_i of Type-III S0 galaxies at 0.2 < z < 0.6 and at z ~ 0 with the stellar mass. The solid vertical black lines in the left panel represent the fixed value at which we compare the linear fits in the right one. Right column: comparison of the PDDs of the scale lengths h_i, h_o and the ratio h_o /h_i at fixed stellar mass log₁₀(M∕M_⊙) = 10.5. Grey histogram with black solid line: PDDs for the Type-III S0 galaxies in the local Universe selected from E08 and G11 samples. Red histogram with dashed line: PDDs for the Type-III S0 galaxies at 0.4 < z < 0.6 from the SHARDS sample. The probabilities (p-value) for both samples to have compatible values at fixed stellar mass of log₁₀(M∕M_⊙) = 10.5 are p = 0.397 (h_i), p = 0.272 (h_o) and p = 0.247 (h_o /h_i). We refer to the legend in the panels for a key of the different lines and symbols.