  We construct for every proper algebraic space over a ground field an Albanese
map to a para-abelian variety, which is unique up to unique isomorphism. This
holds in the absence of rational points or ample sheaves, and also for
reducible or non-reduced spaces, under the mere assumption that the structure
morphism is in Stein factorization. It also works under suitable assumptions in
families. In fact the treatment of the relative setting is crucial, even to
understand the situation over ground fields. This also ensures that Albanese
maps are equivariant with respect to actions of group schemes. Our approach
depends on the notion of families of para-abelian varieties, where each
geometric fiber admits the structure of an abelian variety, and
representability of tau-parts in relative Picard groups, together with
structure results on algebraic groups.
