  We construct models for the rotation rates of T Tauri stars whose spin is
regulated by magnetic linkage between the star and a surrounding accretion
disc. Our models utilise a time-dependent disc code to follow the accretion
process and include the effects of pre-main-sequence stellar evolution. We find
that the initial disc mass controls the evolution of the star-disc system. For
sufficiently massive discs, a stellar field of $\sim$ 1 kG is able to regulate
the spin rate to the observed values during the classical T Tauri phase. The
field then acts to expel the disc and the star spins up at constant angular
momentum as a weak-line system. Lower mass discs are ejected at an early epoch
and fail to brake the star significantly. We extend the model to close binary
systems, and find that the removal of angular momentum from the disc by the
secondary significantly prolongs the inner disc lifetime. Such systems should
therefore be relatively slow rotators. We also discuss the implications of our
model for the spectral energy distributions and variability of T Tauri stars.
