  For a semisimple real Lie group $G$, we study topological properties of
moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface
with a divisor of finitely many distinct points. For a split real form of a
complex simple Lie group, we compute the dimension of apparent parabolic
Teichm{\"u}ller components. In the case of isometry groups of classical
Hermitian symmetric spaces of tube type, we provide new topological invariants
for maximal parabolic $G$-Higgs bundles arising from a correspondence to
orbifold Higgs bundles. Using orbifold cohomology we count the least number of
connected components of moduli spaces of such objects. We further exhibit an
alternative explanation of fundamental results on counting components in the
absence of a parabolic structure.
