  We explore the effects of stellar population models on estimating star
formation histories, ages and masses of high redshift galaxies. The focus is on
the Thermally-Pulsing Asymptotic Giant Branch (TP-AGB) phase of stellar
evolution, whose treatment is a source of major discrepancy among different
evolutionary population synthesis. In particular, besides the models usually
adopted in the literature, we use models (by Maraston 2005), in which the
contribution of the TP-AGB phase is observationally calibrated and is the
dominant source of near-IR energy for stellar populations in the age range 0.2
to 2 Gyr. We use a sample of high-z galaxies in the HUDF, with spectroscopic
redshifts, and Spitzer IRAC and MIPS photometry from GOODS. We find that the
TP-AGB phase plays a key role in the interpretation of Spitzer data for high-z
galaxies, when the rest-frame near-IR is sampled. When fitting without dust
reddening, the models with the empirically-calibrated TP-AGB phase always
reproduce better the observed spectral energy distributions (SEDs). Allowing
for dust reddening improves the fits with literature models in some cases. In
both cases, the results from Maraston models imply younger ages by factors up
to 6 and lower stellar masses (by ~60 % on average). The observed strengths of
the MgUV spectral feature compare better to the predicted ones in the case of
the Maraston models, implying a better overall consistency of SED fitting.
Finally, we find that photometric redshifts improve significantly using these
models on the SEDs extending over the IRAC bands. This work provides the first
direct evidence of TP-AGB stars in the primeval Universe.
