Tobias Goerdt (1), A. Dekel (1), A. Sternberg (2), D. Ceverino (1), R. Teyssier (3), J.R. Primack (4) (1: HU Jerusalem, 2: Tel Aviv U, 3: U Zurich, 4: UCSC) We use high-res cosmological hydro AMR simulations to predict the hydrogen Lalpha emission from the cold gas streams that fed galaxies in massive haloes at high z. The local emissivities due to collisional excitation are calculated from the simulated gas properties, while photoionization is less important. The Lalpha surface density is mapped assuming that 85% of the Lalpha photons are observed. Typical haloes of mass Mv~10^{12-13}Msun at z ~ 3 emit as Lalpha blobs (LABs) with luminosities 10^{43-44} erg/s and 50-100kpc extent. Most of the Lalpha comes from the extended, narrow, partly clumpy, inflowing, cold streams of (1-5)*10^4K that feed the galaxy. Dust absorption is negligible in the streams. The predicted LAB morphology is irregular, with dense clumps and elongated extensions. The area contained within isophotes with surface brightnesses of 2.2*10^{-18} erg s^{-1} cm^{-2} arcsec^{-2} is ~20-200 arcsec^2. The linewidth is expected to range from a few hundreds to above 1000 km/s with a large variance. The typical Lalpha surface brightness profile is proportional to r^{-1.2}. The Lalpha emission in our simulations is powered by the gravitational energy gained by the streaming into the halo potential well, while the UV background contributes <20%. A toy model of gravitational heating explains the simulated results. The simulated LABs are similar in luminosity, morphology and extent to the observed LABs, and they have distinct kinematic features. The predicted luminosity function is consistent with observations, and the predicted areas and linewidths reproduce the observed scaling relations. The LABs can be regarded as direct detections of the cold streams that drive galaxy evolution at high z. This mechanism for producing LABs appears inevitable in most high-z galaxies.