  The nature of some GRB host galaxies has been investigated by means of
chemical evolution models of galaxies of different morphological type following
the evolution of the abundances of H, He, C, N, O, $\alpha$-elements, Ni, Fe,
Zn, and including also the evolution of dust. By comparing predictions with
abundance data, we were able to constrain nature and age of GRB hosts. We also
computed a theoretical cosmic dust rate, including stellar dust production,
accretion and destruction, under the hypotheses of pure luminosity evolution
and strong number density evolution of galaxies. We suggest that one of the
three GRB hosts is a massive proto-spheroid catched during its formation, while
for the other two the situation is more uncertain, although one could perhaps
be a spheroid and the other a spiral galaxy. We estimated the chemical ages of
the host galaxies which vary from 15 to 320 Myr. Concerning the cosmic
effective dust production rate in an unitary volume of the Universe, our
results show that in the case of pure luminosity evolution there is a first
peak between redshift $z=8$ and $9$ and another at $z\sim 5$, whereas in the
case of strong number density evolution it increases slightly from $z=10$ to
$z\sim 2$ and then it decreases down to $z=0$. Finally, we found tha the total
cosmic dust mass density at the present time is: $\Omega_{dust} \sim 3.5\cdot
10^{-5}$in the case of pure luminosity evolution and $\Omega_{dust} \sim 7\cdot
10^{-5}$ in the case of number density evolution.
