  We present the new semi-analytic model of galaxy evolution, DARK SAGE, a
heavily modified version of the publicly available SAGE code. The model is
designed for detailed evolution of galactic discs. We evolve discs in a series
of annuli with fixed specific angular momentum, which allows us to make
predictions for the radial and angular-momentum structure of galaxies. Most
physical processes, including all channels of star formation and associated
feedback, are performed in these annuli. We present the surface density
profiles of our model spiral galaxies, both as a function of radius and
specific angular momentum, and find the discs naturally build a
pseduobulge-like component. Our main results are focussed on predictions
relating to the integrated mass--specific angular momentum relation of stellar
discs. The model produces a distinct sequence between these properties in
remarkable agreement with recent observational literature. We investigate the
impact Toomre disc instabilities have on shaping this sequence and find they
are crucial for regulating both the mass and spin of discs. Without
instabilities, high-mass discs would be systematically deficient in specific
angular momentum by a factor of ~2.5, with increased scatter. Instabilities
also appear to drive the direction in which the mass--spin sequence of spiral
galaxy discs evolves. With them, we find galaxies of fixed mass have higher
specific angular momentum at later epochs.
