  The zoology of singularities for Lorentzian manifold is slightly more
complicated than for Riemannian manifolds. Our present work study
Cauchy-compact globally hyperbolic singular flat spacetimes with extreme
BTZ-like singular lines. We use the notion of BTZ-extension of a singular
spacetime introduced in a previous paper to give a description of Moduli spaces
of such manifolds in term of common Teichm{\"u}ller spaces. This description is
used to construct convex polyhedral cauchy-surface in Cauchy-compact flat
spacetimes with BTZ.
