  This paper dwells upon two aspects of affine supergroup theory, investigating
the links among them.
  First, I discuss the "splitting" properties of affine supergroups, i.e.
special kinds of factorizations they may admit - either globally, or pointwise.
  Second, I present a new contribution to the study of affine supergroups by
means of super Harish-Chandra pairs (a method already introduced by Koszul, and
later extended by other authors). Namely, I provide an explicit, functorial
construction \Psi which, with each super Harish-Chandra pair, associates an
affine supergroup that is always globally strongly split (in short, gs-split) -
thus setting a link with the first part of the paper. On the other hand, there
exists a natural functor \Phi from affine supergroups to super Harish-Chandra
pairs: then I show that the new functor \Psi - which goes the other way round -
is indeed a quasi-inverse to \Phi, provided we restrict our attention to the
subcategory of affine supergroups that are gs-split. Therefore, (the
restrictions of) \Phi and \Psi are equivalences between the categories of
gs-split affine supergroups and of super Harish-Chandra pairs. Such a result
was known in other contexts, such as the smooth differential or the complex
analytic one, or in some special cases, via different approaches: the novelty
in the present paper lies in that I construct a different functor \Psi and thus
extend the result to a much larger setup, with a totally different, more
geometrical method (very concrete indeed, and characteristic free).
  The case of linear algebraic groups is treated also as an intermediate,
inspiring step.
  Some examples, applications and further generalizations are presented at the
end of the paper.
