Every non-singular algebraic curve C has a jacobian J, which is a smooth projective group variety. Given a family of non-singular curves one can construct a family of jacobians. We are interested in what happens to the family of jacobians when the family of non-singular curves degenerates to a singular curve. In the case where the base-space of the family has dimension 1, this is completely understood due to work of André Néron in the 1960s. However, when the base space has higher dimension things become more difficult. We describe a seemingly-new combinatorial invariant which controls these degenerations. In the case of the jacobian of the universal stable curve, we will use this to construct a `minimal’ base-change after which a Néron model exists.