  Observed galactic disks have specific angular momenta similar to expectations
for typical dark matter halos in $\Lambda$CDM. Cosmological hydrodynamical
simulations have recently reproduced this similarity in large galaxy samples by
including strong galactic winds, but the exact mechanism that achieves this is
not yet clear. Here we present an analysis of key aspects contributing to this
relation: angular momentum selection and evolution of Lagrangian mass elements
as they accrete onto dark matter halos, condense into Milky Way-scale galaxies,
and join the $z=0$ stellar phase. We contrast this evolution in the Illustris
simulation with that in a simulation without galactic winds, where the $z=0$
angular momentum is $\approx0.6$ dex lower. We find that winds induce
differences between these simulations in several ways: increasing angular
momentum, preventing angular momentum loss, and causing $z=0$ stars to sample
the accretion-time angular momentum distribution of baryons in a biased way. In
both simulations, gas loses on average $\approx0.4$ dex between accreting onto
halos and first accreting onto central galaxies. In Illustris, this is followed
by $\approx0.2$ dex gains in the `galactic wind fountain' and no further net
evolution past the final accretion onto the galaxy. Without feedback, further
losses of $\approx0.2$ dex occur in the gas phase inside the galaxies. An
additional $\approx0.15$ dex difference arises from feedback preferentially
selecting higher angular momentum gas at accretion by expelling gas that is
poorly aligned. These and additional effects of similar magnitude are
discussed, suggesting a complex origin of the similarity between the specific
angular momenta of galactic disks and typical halos.
