  We determined C, N and alpha-element relative abundances in the gas
surrounding six QSOs at an average redshift of < z > ~ 2.4, by studying six
narrow associated absorption systems in UVES high-resolution spectra. We found
five systems with a metallicity (measured by C/H) consistent or above the solar
value. The ionization structure observed in the associated systems is clearly
different from that of the intervening ones, indicating that the associated
systems are influenced by the strong UV flux from the QSO. There is a possible
correlation (anticorrelation) between [N/C] ([Si/C]) and [C/H] of the studied
associated systems, and [N/C] >= 0 when [C/H] >= 0. We have compared these
observational results with the predictions of a model simulating the joint
evolution of QSOs and their spheroidal hosts. The agreement turns out to be
very good, in particular, the case envisaging massive haloes and high
star-formation rates recovers both the correlation between [N/C] and [C/H] and
the anticorrelation for [Si/C] vs. [C/H]. Narrow associated absorption systems
prove to be powerful tracers of the chemical abundances in gas belonging to
high redshift spheroidal galaxies. The outflow of this same gas, triggered by
the QSO feedback, is probably going to contribute to the early enrichment of
the surrounding intergalactic medium. A larger statistics, possibly increasing
the number of ionisation stages, chemical elements and the redshift range,
would allow us to put firm constraints on detailed chemical evolution models of
galaxies at high redshifts.
