[abridged] We propose a tiered, UV--near-IR, cosmological broad- and medium-band imaging and grism survey that covers ~10 deg^2 in two epochs to m_AB=28, ~3 deg^2 in seven epochs to m_AB=28, and ~1 deg^2 in 20 epochs to m_AB=30 mag. Such a survey is an essential complement to JWST surveys ( 1100nm and z>~8). We aim to: (1) understand in how galaxies formed from perturbations in the primordial density field by studying faint Ly\alpha-emitting and Lyman-break galaxies at 5.5 ~5x10^6 galaxies; (5) trace the strongly epoch-dependent galaxy merger rate and constrain how Dark Energy affected galaxy assembly and the growth of SMBHs; (6) study >~10^5 weak AGN/feeding SMBHs in the faint-end of the QSO LF, over 10 deg^2 and measure how the growth of SMBHs kept pace with galaxy assembly and spheroid growth, and how this process was shaped by various feedback processes over cosmic times since z~8. The proposed study is not feasible with current instrumentation but argues for a wide-field (>~250 arcmin^2), high-resolution (<~0.02--0.11 [300--1700 nm]), UV--near-IR imaging facility on a 4m-class space observatory.