  Current observational results show that both late-and-early-type galaxies
follow tight mass-size planes, on which physical properties such as age,
velocity dispersion and metallicities correlate with the scatter on the plane.
We study the mass-size plane of galaxies in cosmological hydrodynamical
simulations, as a function of velocity dispersion, age, chemical abundances,
ellipticity and spin parameters with the aim at assessing to what extent the
current cosmological paradigm can reproduce these observations and provide a
physical interpretation of them. We select a sample of well-resolved galaxies
from the (100 Mpc)^3 simulation of the EAGLE Project. This sample is composed
by 508 spheroid-dominated galaxies and 1213 disc-dominated galaxies. The
distributions of velocity dispersion, age, metallicity indicators and gradients
and spin parameters across the mass-size plane are analysed. Furthermore, we
study the relation between shape and kinematic parameters. The results are
compared with observations. The mass-weighted ages of the EAGLE galaxies are
found to vary along lines of constant velocity dispersion on the mass-size
plane, except for galaxies with velocity dispersion larger than aprox 150 km
s^(-1) . Negative age gradients tend to be found in extended disc galaxies in
agreement with observations. However, the age distributions of early-type
galaxies show a larger fraction with inverted radial profiles. The distribution
of metallicity gradients does not show any clear dependence on this plane.
Galaxies with similar spin parameters ({\lambda}) display larger sizes as their
dynamical masses increase. Stellar-weighted ages are found to be good proxies
for {\lambda} in galaxies with low ellipticity ({\epsilon}). Abridged
