We study (relative) K-Mittag-Leffler modules, with emphasis on the class K of
absolutely pure modules. A final goal is to describe the K-Mittag-Leffler
abelian groups as those that are, modulo their torsion part, aleph_1-free,
Cor.6.12. Several more general results of independent interest are derived on
the way. In particular, every flat K-Mittag-Leffler module (for K as before) is
Mittag-Leffler, Thm.3.9. A question about the definable subcategories generated
by the divisible modules and the torsion-free modules, resp., has been left
open, Quest.4.6