Compactified Jacobians of Neron type

We characterize stable curves X whose compactified degree-d Jacobian is of Neron type. This means the following: for any one-parameter regular smoothing of X, the special fiber of the Neron model of the Jacobian is isomorphic to a dense open subset of the degree-d compactified Jacobian of X. It is well known that compactified Jacobians of Neron type have the best modular properties, and that they are endowed with a mapping property useful for applications.