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We study the angular-momentum (AM) buildup in high-$z$ massive galaxies usinghigh-resolution cosmological simulations. The AM originates in co-planarstreams of cold gas and merging galaxies tracing cosmic-web filaments, and itundergoes four phases of evolution. (I) Outside the halo virial radius ($R_{\rmv}\!\sim\!100\,{\rm kpc}$), the elongated streams gain AM by tidal torques witha specific AM (sAM) $\sim\!1.7$ times the dark-matter (DM) spin due to the gas'higher quadrupole moment. This AM is expressed as stream impact parameters,from $\sim\!0.3R_{\rm v}$ to counter rotation. (II) In the outer halo, whilethe incoming DM mixes with the existing halo of lower sAM to a spin$\lambda_{\rm dm}\!\sim\!0.04$, the cold streams transport the AM to the innerhalo such that their spin in the halo is $\sim\!3\lambda_{\rm dm}$. (III) Nearpericenter, the streams dissipate into an irregular rotating ring extending to$\sim\!0.3R_{\rm v}$ and tilted relative to the inner disc. Torques exertedpartly by the disc make the ring gas lose AM, spiral in, and settle into thedisc within one orbit. The ring is observable with 30\% probability as a dampedLyman-$\alpha$ absorber. (IV) Within the disc, $<\!0.1R_{\rm v}$, torquesassociated with violent disc instability drive AM out and baryons into acentral bulge, while outflows remove low-spin gas, introducing certainsensitivity to feedback strength. Despite the different AM histories of gas andDM, the disc spin is comparable to the DM-halo spin. Counter rotation canstrongly affect disc evolution.

Four phases of angular-momentum buildup in high-z galaxies: from cosmic-web streams through an extended ring to disc and bulge