We present nucleosynthesis calculations and the resulting 19F stellar yields for a large set of models with different masses and metallicity. We find that the production of fluorine depends on the temperature of the convective pulses, the amount of primary 12C mixed into the envelope by third dredge up and the extent of the partial mixing zone. Then we perform a detailed analysis of the reaction rates involved in the production of 19F and the effects of their uncertainties. We find that the major uncertainties are associated with the 14C(alpha,gamma)18O and the 19F(alpha,p)22Ne reaction rates. For these two reactions we present new estimates of the rates and their uncertainties. The importance of the partial mixing zone is reduced when using our estimate for the 14C(alpha,gamma)18O rate. Taking into account both the uncertainties related to the partial mixing zone and those related to nuclear reactions, the highest values of 19F enhancements observed in AGB stars are not matched by the models. This is a problem that will have to be revised by providing a better understanding of the formation and nucleosynthesis in the partial mixing zone, also in relation to reducing the uncertainties of the 14C(alpha,gamma)18O reaction rate. At the same time the possible effect of Cool Bottom Processing at the base of the convective envelope should be included in the computation of AGB nucleosynthesis. This process could in principle help matching the highest 19F abundances observed by decreasing the C/O ratio at the surface of the star, while leaving the 19F abundance unchanged.
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