We use galaxy catalogues constructed by combining high-resolution N-body simulations with semi-analytic models of galaxy formation to study the properties of Long Gamma-Ray Burst (LGRB) host galaxies. We assume that LGRBs originate from the death of massive young stars and analyse how results are affected by different metallicity constraints on the progenitor stars. As expected, the host sample with no metallicity restriction on the progenitor stars provides a perfect tracer of the cosmic star formation history. When LGRBs are required to be generated by low-metallicity stars, they trace a decreasing fraction of the cosmic star formation rate at lower redshift, as a consequence of the global increase in metallicity. We study the properties of host galaxies up to high redshift (~9), finding that they typically have low-metallicity (Z<0.5 Z_sun) and that they are small (M<10^9 M_sun), bluer and younger than the average galaxy population, in agreement with observational data. They are also less clustered than typical L_* galaxies in the Universe, and their descendents are massive, red and reside in groups of galaxies with halo mass between 10^{13} M_sun to 10^{14} M_sun.
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