Compactified Picard stacks over ${\bar{\mathcal{M}}}_g$

We study algebraic (Artin) stacks over ${\bar{\mathcal{M}}}_g$ giving a functorial way of compactifying the relative degree $d$ Picard variety for families of stable curves. We also describe for every $d$ the locus of genus $g$ stable curves over which we get Deligne-Mumford stacks strongly representable over ${\bar{\mathcal{M}}}_g$.