© 2014 The Authors. We investigate the physical properties of molecular hydrogen (H2) in isolated and interacting disc galaxies with different masses and Hubble types by using chemodynamical simulations with H2 formation on dust grains and dust growth and destruction in interstellar medium. We particularly focus on the dependences of H2 gas mass fractions (fH2), spatial distributions of H I and H2, and local H2-scaling relations on initial halomasses (Mh), baryonic fractions (fbary), gas mass fractions (fg), and Hubble types. The principal results are as follows. The final fH2 can be larger in disc galaxies with higher Mh, fbary, and fg. Some low-mass discmodels with Mh smaller than 1010M⊙ show extremely low fH2 and thus no/little star formation, even if initial fg is quite large (>0.9). Big galactic bulges can severely suppress the formation of H2 from H I on dust grains whereas strong stellar bars cannot only enhance fH2 but also be responsible for the formation of H2-dominated central rings. The projected radial distributions of H2 are significantly more compact than those of H I and the simulated radial profiles of H2-to-H Iratios (Rmol) follow roughly R-1.5 in Milky Way-type disc models. Galaxy interaction can significantly increase fH2 and total H2 mass in disc galaxies. The local surface mass densities of H2 can be correlated with those of dust in a galaxy. The observed correlation between Rmol and gas pressure (Rmol ∝ P0.92 g) can be well reproduced in the simulated disc galaxies.