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We study the evolution of Milky Way thick and thin discs in the light of the most recent observational data. In particular, we analyze abundance gradients of O, N, Fe and Mg along the thin disc as well as the [Mg/Fe] vs. [Fe/H] relations and the metallicity distribution functions at different Galactocentric distances. We run several models starting from the two-infall paradigm, assuming that the thick and thin discs formed by means of two different infall episodes, and we explore several physical parameters, such as radial gas flows, variable efficiency of star formation, different times for the maximum infall onto the disc, different distributions of the total surface mass density of the thick disc and enriched gas infall. Our best model suggests that radial gas flows and variable efficiency of star formation should be acting together with the inside-out mechanism for the thin disc formation. The timescale for maximum infall onto the thin disc, which determines the gap between the formation of the two discs, should be $t_{max}\simeq 3.25$ Gyr. The thick disc should have an exponential, small scale length density profile and gas infall on the inner thin disc should be enriched. We compute also the evolution of Gaia-Enceladus system and study the effects of possible interactions with the thick and thin discs. We conclude that the gas lost by Enceladus or even part of it could have been responsible for the formation of the thick disc but not the thin disc.