  We perform a series of controlled N-body simulations of growing disc galaxies
within non-growing, live dark matter haloes of varying mass and concentration.
Our initial conditions include either a low-mass disc or a compact bulge. New
stellar particles are continuously added on near-circular orbits to the
existing disc, so spiral structure is continuously excited. To study the effect
of combined spiral and giant molecular cloud (GMC) heating on the discs we
introduce massive, short-lived particles that sample a GMC mass function. An
isothermal gas component is introduced for a subset of the models. We perform a
resolution study and vary parameters governing the GMC population, the
histories of star formation and radial scale growth. Models with GMCs and
standard values for the disc mass and halo density provide the right level of
self-gravity to explain the age velocity dispersion relation of the Solar
neighbourhood (Snhd). GMC heating generates remarkably exponential vertical
profiles with scaleheights that are radially constant and agree with
observations of galactic thin discs. GMCs are also capable of significantly
delaying bar formation. The amount of spiral induced radial migration agrees
with what is required for the metallicity distribution of the Snhd. However, in
our standard models the outward migrating populations are not hot enough
vertically to create thick discs. Thick discs can form in models with high
baryon fractions, but the corresponding bars are too long, the young stellar
populations too hot and the discs flare considerably.
