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Theoretical models of AGN radiative feedback predict that AGN-driven, galaxy wide massive outflows are not a rare and peculiar phenomenon, but a fundamental process affecting the bulk of the baryons in the universe. Currently, sparse observational evidence of AGN feedback exists at z>1 but mostly limited to high luminosity objects, therefore a comprehensive picture is still far from being reached. SUPER, aimed at carrying out the first statistically-sound investigation of ionized outflows in AGN host galaxies at the peak epoch of AGN and galaxy assembly, z~2. SUPER is designed to map the ionized gas kinematics ([OIII], Hb, Ha) with ~1 kpc spatial resolution, by exploiting the SINFONI AO capabilities, in a sample probing four orders of magnitude in AGN bolometric luminosity. SUPER will deliver tight scaling relations between the frequency, mass, mass flow rate and momentum rate of ionized outflows, and AGN bolometric luminosity and Eddington ratio, which can be directly plugged into models of galaxy evolution. SUPER will constrain the morphology of different kinematical components, fast outflowing gas versus quiescent star-forming gas, directly probing the effect of outflows on the star-formation processes and galaxy shaping.