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The non-linear evolution of a stratified perturbation in a three dimensionalexpanding Universe is considered. A general Lagrangian scheme (Q model) isintroduced and numerical investigations are performed. The asymptoticcontraction of the core of the agglomeration is studied. A power-law scaling isdetected and an heuristic interpretation of the numerical findings is provided.An asymptotic equation for the multi-stream velocity flow is derived and it isshown to agree quantitatively with the dynamics of the Q model. The relation tothe adhesion model is discussed.Comment: Submitted to Astron. & Astrophy

Asymptotic behavior of a planar perturbation in a three dimensional expanding Universe