We consider Lorentz manifolds which carry a conformal gradient field with at least one zero. All such manifolds are necessarily locally conformally flat. If in addition the manifold is developable and the image of a development map is great enough one can describe the global conformal type by a 3-regular graph provided with two additional datas. We get this conformal invariants using certain conformal development maps into the projective standard quadric. All conformal diffeomorphisms of this projective quadric are nothing else than the projectivities of the ambient real projective space which preserve the quadric. In the proofs we often use this fact. As a by-product of a general existence theorem we give an infinite number of locally conformally flat Lorentz metrics on the differentiable manifold R^n which are in pairs not conformally equivalent.