Context. Lenticular galaxies (S0s) are more likely to host antitruncated (Type III) stellar discs than galaxies of later Hubble types. Major mergers are popularly considered too violent to make these breaks. Aims: We have investigated whether major mergers can result into S0-like remnants with realistic antitruncated stellar discs or not. Methods: We have analysed 67 relaxed S0 and E/S0 remnants resulting from dissipative N-body simulations of major mergers from the GalMer database. We have simulated realistic R-band surface brightness profiles of the remnants to identify those with antitruncated stellar discs. Their inner and outer discs and the breaks have been quantitatively characterized to compare with real data. Results: Nearly 70% of our S0-like remnants are antitruncated, meaning that major mergers that result in S0s have a high probability of producing Type III stellar discs. Our remnants lie on top of the extrapolations of the observational trends (towards brighter magnitudes and higher break radii) in several photometric diagrams, because of the higher luminosities and sizes of the simulations compared to observational samples. In scale-free photometric diagrams, simulations and observations overlap and the remnants reproduce the observational trends, so the physical mechanism after antitruncations is highly scalable. We have found novel photometric scaling relations between the characteristic parameters of the antitruncations in real S0s, which are also reproduced by our simulations. We show that the trends in all the photometric planes can be derived from three basic scaling relations that real and simulated Type III S0s fulfill: hi ∝ RbrkIII, ho ∝ RbrkIII, and μbrkIII ∝ RbrkIII, where hi and ho are the scalelengths of the inner and outer discs, and μbrkIII and RbrkIII are the surface brightness and radius of the breaks. Bars and antitruncations in real S0s are structurally unrelated phenomena according to the studied photometric planes. Conclusions: Major mergers provide a feasible mechanism to form realistic antitruncated S0 galaxies. Table 3 is available in electronic form at http://www.aanda.org