  This article follow the article
{http://hal.archives-ouvertes.fr/hal-00361030/fr/} in which the author
characterize the fact of being of finite volume for a convex projective
surface. We show here that the moduli space $\beta_f(\Sigma_{g,p})$ of the
convex projective structure on the surface $\Sigma_{g,p}$ of genius $g$ with
$p$ punctures is homeomorphic to $\R^{16g-16+6p}$. Finally, we show that
$\beta_f(\Sigma_{g,p})$ can be identify with a connected component of the space
of representation of the fundamental group of $\Sigma_{g,p}$ in $SL(3,R)$ which
keep the parabolic modulo conjugaison.
