We present new theoretical stellar evolutionary models of metal-rich asymptotic giant branch (AGB) stars. Stellar models are evolved with initial masses between 1M ⊙ and 7M ⊙ at Z = 0.007, and 1M ⊙ and 8M ⊙ at Z = 0.014 (solar) and at Z = 0.03. We evolve models with a canonical helium abundance and with helium enriched compositions (Y = 0.30, 0.35, 0.40) at Z = 0.014 and Z = 0.03. The efficiency of third dredge-up and the mass range of carbon stars decreases with an increase in metallicity. We predict carbon stars form from initial masses between 1.75-7M ⊙ at Z = 0.007 and between 2-4.5M ⊙ at solar metallicity. At Z = 0.03 the mass range for C-star production is narrowed to 3.25-4M ⊙ . The third dredge-up is reduced when the helium content of the model increases owing to the reduced number of thermal pulses on the AGB. A small increase of ∆Y = 0.05 is enough to prevent the formation of C stars at Z = 0.03, depending on the mass-loss rate, whereas at Z = 0.014, an increase of ∆Y 0.1 is required to prevent the formation of C stars. We speculate that the probability of finding C stars in a stellar population depends as much on the helium abundance as on the metallicity. To explain the paucity of C stars in the inner region of M31 we conclude that the observed stars have Y 0.35 or that the stellar metallicity is higher than [Fe/H] ≈ 0.1.