  The angular momentum of galactic discs in semi-analytic models of galaxy
formation is usually updated in time as material is accreted to the disc by
adopting a constant dimensionless spin parameter and little attention is paid
to the effects of accretion with misaligned angular momenta. These effects are
the subject of this paper, where we adopt a Monte-Carlo simulation for the
changes in the direction of the angular momentum of a galaxy disc as it
accretes matter based on accurate measurements from dark-matter haloes in the
Millennium II simulation. In our semi-analytic model implementation, the flips
seen the dark matter haloes are assumed to be the same for the cold baryons;
however, we also assume that in the latter the flip also entails a difficulty
for the disc to increase its angular momentum which causes the disc to become
smaller relative to a no-flip case. This makes star formation to occur faster,
specially in low mass galaxies at all redshifts allowing galaxies to reach
higher stellar masses faster. We adopt a new condition for the triggering of
starbursts during mergers. As these produce the largest flips it is natural to
adopt the disc instability criterion to evaluate the triggering of bursts in
mergers instead of one based on mass ratios as in the original model. The new
implementation reduces the average lifetimes of discs by a factor of 2, while
still allowing old ages for the present-day discs of large spiral galaxies. It
also provides a faster decline of star formation in massive galaxies and a
better fit to the bright end of the luminosity function at z = 0.
