  We construct for each proper algebraic space an Albanese map to a
para-abelian variety, which is unique up to unique isomorphism. This holds
unconditionally, in the absence of rational points or ample sheaves, and also
for reducible or non-reduced spaces. It also works in families, at least over
dense open sets of the base. 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.
