We present recent improvements and results of an extensive analysis of the TP-AGB phase performed by means of a synthetic model (Marigo 1998a, b; Marigo et al. 1998a, b). The improvements concern: i) the use of a homogeneous and accurate set of analytical relations (Wagenhuber & Groenewegen 1998); ii) a new treatment of envelope burning in the most massive TP-AGB stars (M > 3.5M ⊙) to account for the possible break-down of the core mass-luminosity relation; iii) a better treatment of the third dredge-up to infer if and when the process takes place.
Extensive calculations of synthetic TP-AGB models have been carried out over the mass range (0.8M ⊙ ÷ 5M ⊙) and for three sets of initial metallicity (Z = 0.019, Z = 0.008, Z = 0.004). The formation of carbon stars is investigated addressing the following issues: a) the reproduction of the observed luminosity functions of carbons stars in both Magellanic Clouds, and b) the formation of very bright and optically obscured carbon stars.