[Abridged] We investigate the global galaxy evolution over 12 Gyr (0.051.7, we set alpha steepening with (1+z). The absolute magnitude M*_FUV brightens in the entire range 02 it is on average brighter than in the literature, while phi* is smaller. Our total LD shows a peak at z=2, present also when considering all sources of uncertainty. The SFRD history peaks as well at z=2. It rises by a factor of 6 during 2 Gyr (from z=4.5 to z=2), and then decreases by a factor of 12 during 10 Gyr down to z=0.05. This peak is mainly produced by a similar peak within the population of galaxies with -21.52 of the SFRD is compelling for models of galaxy formation. The mean dust attenuation A_FUV of the global galaxy population rises by 1 mag during 2 Gyr from z=4.5 to z=2, reaches its maximum at z=1 (A_FUV=2.2 mag), and then decreases by 1.1 mag during 7 Gyr down to z=0. The dust attenuation maximum is reached 2 Gyr after the SFRD peak, implying a contribution from the intermediate-mass stars to the dust production at z