  We analyze the first cosmological simulations that recover the fragmentation
of high-redshift galactic discs driven by cold streams. The fragmentation is
recovered owing to an AMR resolution better than 70 pc with cooling below 10^4
K. We study three typical star-forming galaxies in haloes of approx. 5 10^11
Msun at z=2.3, when they were not undergoing a major merger. The steady gas
supply by cold streams leads to gravitationally unstable, turbulent discs,
which fragment into giant clumps and transient features on a dynamical
timescale. The disc clumps are not associated with dark-matter haloes. The
clumpy discs are self-regulated by gravity in a marginaly unstable state. Clump
migration and angular-momentum transfer on an orbital timescale help the growth
of a central bulge with a mass comparable to the disc. The continuous gas input
keeps the system of clumpy disc and bulge in a near "steady state", for several
Gyr. The average star-formation rate, much of which occurs in the clumps,
follows the gas accretion rate of approx. 45 Msun/yr. The simulated galaxies
resemble in many ways the observed star-forming galaxies at high redshift.
Their properties are consistent with the simple theoretical framework presented
in Dekel, Sari & Ceverino (2009). In particular, a two-component analysis
reveals that the simulated discs are indeed marginally unstable, and the time
evolution confirms the robustness of the clumpy configuration in a cosmological
steady state. By z=1 the simulated systems are stabilized by a dominant stellar
spheroid, demonstrating the process of "morphological quenching" of star
formation (Martig et al. 2009) . We demonstrate that the disc fragmentation is
not a numerical artifact once the Jeans length is kept larger than 7 resolution
elements, i.e. beyond the standard Truelove criterion.
