It has been recently found that the characteristic photometric parameters of antitruncated discs in S0 galaxies follow tight scaling relations. We investigate if similar scaling relations are satisfied by galaxies of other morphological types. We have analysed the trends in several photometric planes relating the characteristic surface brightness and scalelengths of the breaks and the inner and outer discs of local antitruncated S0-Scd galaxies, using published data and fits performed to the surface brightness profiles of two samples of Type-III galaxies in the R and Spitzer 3.6 microns bands. We have performed linear fits to the correlations followed by different galaxy types in each plane, as well as several statistical tests to determine their significance. We have found that: 1) the antitruncated discs of all galaxy types from Sa to Scd obey tight scaling relations both in R and 3.6 microns, as observed in S0s; 2) the majority of these correlations are significant accounting for the numbers of the available data samples; 3) the trends are clearly linear when the characteristic scalelengths are plotted on a logarithmic scale; and 4) the correlations relating the characteristic surface brightnesses of the inner and outer discs and the breaks with the various characteristic scalelengths significantly improve when the latter are normalized to the optical radius of the galaxy. The results suggest that the scaling relations of Type-III discs are independent of the morphological type and the presence (or absence) of bars within the observational uncertainties of the available datasets, although larger and deeper samples are required to confirm this. The tight structural coupling implied by these scaling relations impose strong constraints on the mechanisms proposed for explaining the formation of antitruncated stellar discs in the galaxies across the whole Hubble Sequence (Abridged).
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