Understanding how galaxies form in the early universe and how they evolve through cosmic time is a major goal of modern astrophysics. Panchromatic look-back sky surveys significantly advanced the field in the past decade, and we are now entering a 'golden age' of radio astronomy given an order of magnitude improved facilities like JVLA, ATCA and ALMA. I am leading two unique, state-of-the-art (JVLA/ATCA) radio surveys that will push to the next frontiers. The proposed ERC project will focus on the growth of stellar and black-hole mass in galaxies across cosmic time by: 1-probing various types of extremely faint radio sources over cosmic time, revealing the debated abundance of faint radio sources, 2-exploring star formation conditions at early cosmic times, allowing to access for the first time the dust-unbiased cosmic star formation history since the epoch of reionization, 3-performing the first census of high-redshift starbursting galaxies (SMGs), and their role in galaxy formation and evolution, and 4-performing a full census of galaxies hosting supermassive black holes (AGN), with different black-hole accretion modes, and their roles in galaxy evolution.The exploitation of these radio sky surveys is essential for the preparation and success of the future large facilities like ASKAP, and SKA as they will 1-provide best predictions of the to-date uncertain cosmic radio background seen with the SKA, and 2-optimize photometric redshift estimates, essential for the success of the first ASKAP sky survey (EMU, >2016).My radio surveys, expected to yield >100 refereed publications, carry an immense legacy value. The proposed ERC funding is essential for the success of these timely surveys, which I will conduct from Croatia. The ERC grant will allow me to lead my own research group working on this novel data, and to even more firmly establish myself as a leading survey scientist, and lead my group to internationally competitive levels, and enhance EU competitiveness.