  Let $M$ be a maximal globally hyperbolic Cauchy compact flat spacetime of
dimension 2+1, admitting a Cauchy hypersurface diffeomorphic to a compact
hyperbolic manifold. We study the asymptotic behaviour of level sets of
quasi-concave time functions on $M$. We give a positive answer to a conjecture
of Benedetti and Guadagnini in \cite{MR1857817}. More precisely, we prove that
the level sets of such a time function converge in the Hausdorff-Gromov
equivariant topology to a real tree. Moreover, this limit does not depend on
the choice of the time function.
