Photometric scaling relations in scale-free diagrams of the characteristic surface brightness of the inner and outer discs and breaks (referred to μ_brkIII) with h_i/h_o, for real and simulated Type III S0s. Solid line: linear fit to our simulations sample. Dashed line: linear fit to the observational data by E08 and G11. Dotted line: expected relations derived from the simple observational scaling relations h_i ∝ R_brkIII, h_o ∝ R_brkIII, and μ_brkIII ∝ R_brkIII (see Sect. 3.6). Consult the legend in the figure. (Color version online.)