  We study two different versions of the simple exclusion process on augmented
Galton-Watson trees, the constant speed model and the varying speed model. In
both cases, the simple exclusion process starts from an equilibrium
distribution with non-vanishing particle density. Moreover, we assume to have
initially a particle in the root, the tagged particle. We show for both models
that the tagged particle has a positive linear speed and we give explicit
formulas for the speeds.
