  We give an invariance principle for very general additive functionals of
conditioned Bienaym{\'e}-Galton-Watson trees in the global regime when the
offspring distribution lies in the domain of attraction of a stable
distribution, the limit being an additive functional of a stable L{\'e}vy tree.
This includes the case when the offspring distribution has finite variance (the
L{\'e}vy tree being then the Brownian tree). We also describe, using an
integral test, a phase transition for toll functions depending on the size and
height.
