  We used a new generation of asymptotic giant branch (AGB) stellar models that
include dust formation in the stellar winds to find the links between
evolutionary models and the observed properties of a homogeneous sample of
Large Magellanic Cloud (LMC) planetary nebulae (PNe). Comparison between the
evolutionary yields of elements such as CNO and the corresponding observed
chemical abundances is a powerful tool to shed light on evolutionary processes
such as hot bottom burning (HBB) and third dredge-up (TDU). We found that the
occurrence of HBB is needed to interpret the nitrogen-enriched (log(N/H)+12>8)
PNe. In particular, N-rich PNe with the lowest carbon content are nicely
reproduced by AGB models of mass M >=6 Mo, whose surface chemistry reflects the
pure effects of HBB. PNe with log(N/H)+12<7.5 correspond to ejecta of stars
that have not experienced HBB, with initial mass below about 3 Mo. Some of
these stars show very large carbon abundances, owing to the many TDU episodes
experienced. We found from our LMC PN sample that there is a threshold to the
amount of carbon accumulated at AGB surfaces, log(C/H)+12<9. Confirmation of
this constraint would indicate that, after the C-star stage is reached,AGBs
experience only a few thermal pulses, which suggests a rapid loss of the
external mantle, probably owing to the effects of radiation pressure on
carbonaceous dust particles present in the circumstellar envelope. The
implications of these findings for AGB evolution theories and the need to
extend the PN sample currently available are discussed.
