  By means of galaxy evolutionary models, we explore the direct consequences of
the LCDM cosmogony on the size evolution of galactic discs, avoiding
intentionally the introduction of intermediate (uncertain) astrophysical
processes. Based on the shape of the rotation curves and guided by a simplicity
criterion, we adopt an average galaxy mass baryon fraction of 0.03. In order to
study general behaviors, only models with the average initial conditions are
analyzed. The stellar and B-band effective radii, R* and RB, of individual
galaxies grow significantly with time (inside-out disc formation) with laws
that are weakly dependent on mass, M*,or luminosity, LB. However, the change of
R* with z at fixed M* is slow; for z<2.5, R*(M*=const) ~ (1+z)^-0.4. On the
other hand, the change of RB with z at a fixed LB is strong and resembles the
RB decreasing law of the individual models; roughly RB(LB=const) ~ (1+z)^-0.85
for z<0.75, and ~(1+z)^-1.1 for z>0.75. We find also that at z=0, R* ~ M*^0.38
and RB ~ LB^0.40, remaining the slopes of these relations almost the same up to
z ~ 3. Our predictions are in reasonable agreement with observational
inferences on the typical radius change with z of late-type galaxies more
luminous (massive) than high values imposed by the selection effects. The
models seem also to be consistent, within the large scatter, with the RB and LB
values obtained from non complete samples of sub-L* late-type galaxies with
available rest-frame photometric information at different z's. The properties
and evolution of the LCDM haloes seem to be the main drivers of galaxy disc
size evolution. Nevertheless, the models reveal a potential difficulty in
explaining the observed steepening of the RB-LB relation with respect to the
R*-M* one, an effect related to the well established color-magnitude relation.
