The results obtained in Paper I are used to study possible relationships between the truncation radius of stellar discs in the NIR and structural parameters of the galaxies. The NIR truncation radius is larger for brighter galaxies, being proportional to V_mc with c ≈ 3/2, and with Vm being the asymptotic rotation velocity at large radii (when the rotation curve becomes flat), and is lower for higher wavelengths. When it is normalized to the scalelength, the truncation is an increasing function of the central surface brightness and is lower for late type galaxies, although these correlations are weaker. These relations are in agreement with the scenario of magnetically driven truncations.