  We study parabolic G-Higgs bundles over a compact Riemann surface with fixed
punctures, when G is a real reductive Lie group, and establish a correspondence
between these objects and representations of the fundamental group of the
punctured surface in G with arbitrary holonomy around the punctures. Three
interesting features are the relation between the parabolic degree and the
geometry of the Tits boundary, the treatment of the case when the logarithm of
the monodromy is on the boundary of a Weyl alcove, and the correspondence of
the orbits encoding the singularity via the Kostant-Sekiguchi correspondence.
We also describe some special features of the moduli spaces when G is a split
real form or a group of Hermitian type.
