  We use high-resolution cosmological hydrodynamical AMR simulations to predict
the characteristics of La emission from the cold gas streams that fed galaxies
in massive haloes at high redshift. The La luminosity in our simulations is
powered by the release of gravitational energy as gas flows from the
intergalactic medium into the halo potential wells. The UV background
contributes only <20% to the gas heating. The La emissivity is due primarily to
electron-impact excitation cooling radiation in gas ~2x10^4K. We calculate the
La emissivities assuming collisional ionisation equilibrium (CIE) at all gas
temperatures. The simulated streams are self-shielded against the UV
background, so photoionisation and recombination contribute negligibly to the
La line formation. We produce theoretical maps of the La surface brightnesses,
assuming that ~85% of the La photons are directly observable. We find that
typical haloes of mass Mv~10^12-13 Msun at z~3 emit as La blobs (LABs) with
luminosities 10^43-44 erg/s. Most of the La comes from the extended narrow,
partly clumpy, inflowing, cold streams that feed the growing galaxies. The
predicted LAB morphology is therefore irregular, with dense clumps and
elongated extensions. The linewidth is expected to range from 10^2 to more than
10^3 km/s with a large variance. The typical La surface brightness profile is
proportional to r^-1.2 where r is the distance from the halo centre. Our
simulated LABs are similar in luminosity, morphology and extent to the observed
LABs, with distinct kinematic features. The predicted La luminosity function is
consistent with observations, and the predicted areas and linewidths roughly
recover the observed scaling relations. This mechanism for producing LABs
appears inevitable in many high-z galaxies. Some of the LABs may thus be
regarded as direct detections of the cold streams that drove galaxy evolution
at high z.
