  We prove that there exist some stacks, representable over the stack of stable
curves, having the following universal property with respect to N\'eron models
of Jacobians. For every one-parameter family of stable curves, with regular
total space, the N\'eron model of the Jacobian of its generic fibre is
isomorphic to the base change of the above stacks via the moduli map of the
given family. We also obtain a stack compactification of the universal Picard
scheme and hence a geometrically meaningful completion of the N\'eron model of
the Jacobian for every family as above.
