  We investigate the cross-talk between the two key components of tidal-torque
theory, the inertia (I) and shear (T) tensors, using a cosmological N-body
simulation with thousands of well-resolved haloes. We find that the principal
axes of I and T are strongly aligned, even though I characterizes the
proto-halo locally while T is determined by the large-scale structure. Thus,
the resultant galactic spin, which plays a key role in galaxy formation, is
only a residual due to ~10 per cent deviations from perfect alignment of T and
I. The T-I correlation induces a weak tendency for the proto-halo spin to be
perpendicular to the major axes of T and I, but this correlation is erased by
non-linear effects at late times, making the observed spins poor indicators of
the initial shear field. However, the T-I correlation implies that the shear
tensor can be used for identifying the positions and boundaries of proto-haloes
in cosmological initial conditions -- a missing piece in galaxy formation
theory. The typical configuration is of a prolate proto-halo lying
perpendicular to a large-scale high-density ridge, with the surrounding voids
inducing compression along the major and intermediate inertia axes of the
proto-halo. This leads to a transient sub-halo filament along the large-scale
ridge, whose sub-clumps then flow along the filament and merge into the final
halo. The centres of proto-haloes tend to lie in ~1 sigma over-density regions,
but their association with linear density maxima smoothed on galactic scales is
vague: only ~40 per cent of the proto-haloes contain peaks within them. Several
other characteristics distinguish proto-haloes from density peaks, e.g., they
tend to compress along two principal axes while many peaks compress along three
axes.
