In this paper, we propose a nonparametric estimation strategy for the conditional density function of Y given X, from independent and identically distributed observations (Xi, Yi) 1≤i≤n. We consider a regression strategy related to projection subspaces of L 2 generated by non compactly supported bases. This rst study is then extended to the case where Y is not directly observed, but only Z = Y + ε, where ε is a noise with known density. In these two settings, we build and study collections of estimators, compute their rates of convergence on anisotropic space on non-compact supports, and prove related lower bounds. Then, we consider adaptive estimators for which we also prove risk bounds.