  Models of disc galaxies which invoke viscosity-driven radial flows have long
been known to provide a natural explanation for the origin of stellar
exponential discs, under the assumption that the star formation and viscous
timescales are comparable. We present models which invoke simultaneous star
formation, viscous redistribution of gas and cosmologically-motivated gaseous
infall and explore the predictions such models make for the scale length
evolution and radial star formation history of galactic stellar discs. While
the inclusion of viscous flows is essential for ensuring that the stellar disc
is always exponential over a significant range in radius, we find that such
flows play essentially no role in determining the evolution of the disc scale
length. In models in which the main infall phase precedes the onset of star
formation and viscous evolution, we find the exponential scale length to be
rather invariant with time. On the other hand, models in which star
formation/viscous evolution and infall occur concurrently result in a smoothly
increasing scale length with time, reflecting the mean angular momentum of
material which has fallen in at any given epoch. The disc stellar populations
in these models are predominantly young (ie. ages < 5 Gyr) beyond a few scale
lengths. In both cases, viscous flows are entirely responsible for transporting
material to very large radii. We discuss existing observational constraints on
these models from studies of both local and moderate redshift disc galaxies. In
particular, a good agreement is found between the solar neighbourhood star
formation history predicted by our infall model and the recent observational
determination of this quantity by Rocha-Pinto et al (2000).
