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 non-linear growth of structures for cold dark matter (CDM) and neutrino fluids in the context of growing neutrino cosmologies. Our analysis shows a pulsation increase and subsequent decrease in the neutrino density contrast. This could lead to interesting observational signatures, as an enhanced bulk flow in a situation where the DM density contrast differs only very mildly from the standard ΛCDM 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.