We present deep, near-infrared HST/WFC3 grism spectroscopy and imaging for a sample of 14 galaxies at z~2 selected from a mass-complete photometric catalog in the COSMOS field. By combining the grism observations with photometry in 30 bands, we deriv
e accurate constraints on their redshifts, stellar masses, ages, dust extinction and formation redshifts. We show that the slope and scatter of the z~2 mass-size relation of quiescent galaxies is consistent with the local relation, and confirm previous findings that the sizes for a given mass are smaller by a factor of two to three. Finally, we show that the observed evolution of the mass-size relation of quiescent galaxies between z=2 and 0 can be explained by quenching of increasingly larger star-forming galaxies, at a rate dictated by the increase in the number density of quiescent galaxies with decreasing redshift. However, we find that the scatter in the mass-size relation should increase in the quenching-driven scenario in contrast to what is seen in the data. This suggests that merging is not needed to explain the evolution of the median mass-size relation of massive galaxies, but may still be required to tighten its scatter, and explain the size growth of individual z=2 galaxies quiescent galaxies.
