  An Adaptive Mesh Refinement cosmological resimulation is analyzed in order to
test whether filamentary flows of cold gas are responsible for the build-up of
angular momentum within a Milky Way like disk at z>=3. A set of algorithms is
presented that takes advantage of the high spatial resolution of the simulation
(12 pc) to identify: (i) the central gas disk and its plane of orientation;
(ii) the complex individual filament trajectories that connect to the disk,
and; (iii) the infalling satellites. The results show that two filaments at
z>5.5, which later merge to form a single filament at z<4, drive the angular
momentum and mass budget of the disk throughout its evolution, whereas luminous
satellite mergers make negligible fractional contributions. Combined with the
ubiquitous presence of such filaments in all large-scale cosmological
simulations that include hydrodynamics, these findings provide strong
quantitative evidence that the growth of thin disks in haloes with masses below
10^{12} M_{sun}, which host the vast majority of galaxies, is supported via
inflowing streams of cold gas at intermediate and high redshifts.
