  We present a semi-analytical model to test the hypothesis that Ly-alpha QSO
absorption lines originate in gaseous halos produced by multiple supernova
explosions occurring in Pop III objects in a CDM cosmological scenario hoping
to assess the validity of CDM models and/or constrain their parameters. The
preliminary results indicate that the range of $N_{HI}$, redshift distribution
and metallicity of clouds are well reproduced by CDM if they are associated
with galaxy halos or groups. Firm conclusions on clouds with $N_{HI}\le 10^{14}
cm^{-2}$ need a more refined study.
