  We evaluate the success of linear tidal-torque theory (TTT) in predicting
galactic-halo spin using a cosmological N-body simulation with thousands of
well-resolved haloes. The proto-haloes are identified by tracing today's haloes
back to the initial conditions. The TTT predictions for the proto-haloes match,
on average, the spin amplitudes of today's virialized haloes if linear growth
is assumed until ~t_0/3, or 55-70 per cent of the halo effective turn-around
time. This makes it a useful qualitative tool for understanding certain average
properties of galaxies, such as total spin and angular-momentum distribution
within haloes, but with a random scatter of the order of the signal itself.
Non-linear changes in spin direction cause a mean error of ~50 degrees in the
TTT prediction at t_0, such that the linear spatial correlations of spins on
scales >~ 1 Mpc/h are significantly weakened by non-linear effects. This
questions the usefulness of TTT for predicting intrinsic alignments in the
context of gravitational lensing. We find that the standard approximations made
in TTT, including a second order expansion of the Zel'dovich potential and a
smoothing of the tidal field, provide close-to-optimal results.
