  Growing Neutrino quintessence describes a form of dynamical dark energy that
could explain why dark energy dominates the universe only in recent
cosmological times. This scenario predicts the formation of large scale
neutrino lumps which could allow for observational tests. We perform for the
first time N-body simulations of the nonlinear growth of structures for cold
dark matter and neutrino fluids in the context of Growing Neutrino cosmologies.
Our analysis shows a pulsation - increase and subsequent decrease - of the
neutrino density contrast. This could lead to interesting observational
signatures, as an enhanced bulk flow in a situation where the dark matter
density contrast only differs very mildly from the standard LCDM scenario. We
also determine for the first time the statistical distribution of neutrino
lumps as a function of mass at different redshifts. Such determination provides
an essential ingredient for a realistic estimate of the observational
signatures of Growing Neutrino cosmologies. Due to a breakdown of the
non-relativistic Newtonian approximation our results are limited to redshifts z
> 1.
