  We give a new proof of Raynaud-Gruson's theorem regarding flattening by
blow-ups. The proof is direct, by working directly on the inverse limit of
admissible blow-ups, which is a valuative space similar to the classical
Zariski-Riemann space. These valuative spaces are defined in a broader context
and always have an analogous flattening property: this yields a generalization
of Raynaud-Gruson's theorem.
