The fully unintegrated, off-diagonal quark-quark correlator for a spin-1/2
hadron is parameterized in terms of so-called generalized parton correlation
functions. Such objects, in particular, can be considered as mother
distributions of generalized parton distributions on the one hand and
transverse momentum dependent parton distributions on the other. Therefore, our
study provides new, model-independent insights into the recently proposed
nontrivial relations between generalized and transverse momentum dependent
parton distributions. We find that none of these relations can be promoted to a
model-independent status. As a by-product we obtain the first complete
classification of generalized parton distributions beyond leading twist. The
present paper is a natural extension of our previous corresponding analysis for
spin-0 hadrons.Comment: 41 pages, 3 figures; v2: added referenc