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One of the biggest tensions between observations and theory lies in the existence of quiescent ultra-massive galaxies (UMGs) recently confirmed at z>3. Understanding how the star formation activity is halted is one of the most important outstanding problems in galaxy evolution comma but the physics of this quenching remain uncertain. Multiple processes have been proposed with different timescales. The simultaneous measurements of star-formation histories and stellar mass density represent the most promising way to discriminate between them. However comma little is known about the sizes and structures of UMGs at z>3. Recently comma the largest sample to-date of UMGs (Mstar>10elev11 Msun) at 3<z<4 has been spectroscopically confirmed by the MAGAZ3NE survey. The proposed program will provide deep F160W imaging for all MAGAZ3NE UMGs comma enabling the measurement comma for the first time comma of size comma structure comma and central stellar mass density within 1 kpc for a representative sample of 16 spectroscopically confirmed UMGs at 3<z<4. This knowledge will inform us on the formation and quenching mechanisms comma and we will investigate the connection between quenching and morphological transformation. We will constrain the pair fractions comma quantifying systematic effects of blending on the number density of UMGs at 3<z<4 comma which provides very strong constraints on models of galaxy formation. Finally comma for the quiescent UMGs (virgul1-2 of the sample) comma we will derive dynamical masses by combining size and Sersic index measurements with their stellar velocity dispersions comma investigating the dynamical-to-stellar mass ratios and placing constraints on the IMF in 3<z<4 UMGs.