  We extend our previous work focused at $z\sim0$, studying the redshift
evolution of galaxy dynamical properties using the state-of-the-art
semi-analytic model GAEA: we show that the predicted size-mass relation for
disky/star forming and quiescent galaxies is in good agreement with
observational estimates, up to $z\sim2$. Bulge dominated galaxies have sizes
that are offset low with respect to observational estimates, mainly due to our
implementation of disk instability at high redshift. At large masses, both
quiescent and bulge dominated galaxies have sizes smaller than observed. We
interpret this as a consequence of our most massive galaxies having larger gas
masses than observed, and therefore being more affected by dissipation. We
argue that a proper treatment of quasar driven winds is needed to alleviate
this problem. Our model compact galaxies have number densities in agreement
with observational estimates and they form most of their stars in small and low
angular momentum high-$z$ halos. GAEA predicts that a significant fraction of
compact galaxies forming at high-$z$ is bound to merge with larger structures
at lower redshifts: therefore they are not the progenitors of normal-size
passive galaxies at $z=0$. Our model also predicts a stellar-halo size relation
that is in good agreement with observational estimates. The ratio between
stellar size and halo size is proportional to the halo spin and does not depend
on stellar mass but for the most massive galaxies, where AGN feedback leads to
a significant decrease of the retention factor (from about 80 per cent to 20
per cent).
