  We perform controlled N-body simulations of disc galaxies growing within live
dark matter (DM) haloes to present-day galaxies that contain both thin and
thick discs. We consider two types of models: a) thick-disc initial conditions
to which stars on near-circular orbits are continuously added over ~10 Gyr and
b) models in which the birth velocity dispersion of stars decreases
continuously over the same time-scale. We show that both schemes produce
double-exponential vertical profiles similar to that of the Milky Way (MW). We
indicate how the spatial age structure of galaxies can be used to discriminate
between scenarios. We show that the presence of a thick disc significantly
alters and delays bar formation and thus makes possible models with a realistic
bar and a high baryon-to-DM mass ratio in the central regions, as required by
microlensing constraints. We examine how the radial mass distribution in stars
and DM is affected by disc growth and non-axisymmetries. We discuss how bar
buckling shapes the vertical age distribution of thin- and thick-disc stars in
the bar region. The extent to which the combination of observationally
motivated inside-out growth histories and cosmologically motivated dark halo
properties leads to the spontaneous formation of non-axisymmetries that steer
the models towards present-day MW-like galaxies is noteworthy.
