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We calculate the physical conditions and the N/H and O/H relative abundancesfor a sample of long GRB (LGRB) host galaxies in the redshift range 1<z<2.1 bymodelling recently observed line and continuum spectra. The results areconsistent with those previously calculated for LGRB host galaxies throughout amore extended redshift range z<3. We analyse star formation rates (SFR) withinthe LGRB hosts on the basis of the Ha fluxes. They are compared with those oflocal low-luminosity starburst (SB) galaxies, individual HII regions in localgalaxies as well as LGRB host galaxies at intermediate and relatively highredshifts. The enhanced SFR in the HII regions within nearby galaxies isexplained by a relatively high filling factor which characterizes "individualregions" rather than "entire galaxies" which are generally presented by theobservations. The fragmented matter in the galaxies derives from progenitormerging. We check whether the release by the morphological transformations ofice of the O_2 and N_2 molecules trapped into the ice mantles of dust grainscould explain the N/O ratios throughout the redshift. We have found that shockvelocities calculated by modelling the spectra are high enough to completelydestroy the ice mantles. Therefore, the prevention of secondary nitrogenformation is a valid hypothesis to explain the low N/O ratios at z<1. The SFRtrend increasing with z is roughly similar to that of N/O.

Analysis of the spectra observed from GRB061007, GRB061121, GRB080605, GRB090926B, GRB080207 and GRB070521 host galaxies. Ha and SFR trends