  We investigate the transverse-momentum-dependence in semi-inclusive deep
inelastic leptoproduction of hadrons. There are two different theoretical
approaches to study this dependence, one for low and one for high transverse
momentum of the observed hadron. We systematically investigate their
connection, paying special attention to azimuthal distributions and to
polarization dependence. In the region of intermediate transverse momentum,
where both approaches are applicable, we find that their results match for
certain observables but not for others. Interpolating expressions are discussed
for the case where one has no matching. We then use power counting to determine
which mechanism is dominant in various azimuthal and spin asymmetries that are
integrated over the transverse momentum. Our findings have consequences for the
extension of transverse-momentum-dependent factorization beyond leading twist.
They also shed light on the problem of resumming logarithms of transverse
momentum for azimuthal distributions. Our results can be carried over to the
Drell-Yan process and to two-hadron production in e+e- annihilation.
