  We prove that some relative character varieties of the fundamental group of a
punctured sphere into the Hermitian Lie groups $\mathrm{SU}(p,q)$ admit compact
connected components. The representations in these components have several
counter-intuitive properties. For instance, the image of any simple closed
curve is an elliptic element. These results extend a recent work of Deroin and
the first author, which treated the case of $\textrm{PU}(1,1) =
\mathrm{PSL}(2,\mathbb{R})$. Our proof relies on the non-Abelian Hodge
correspondance between relative character varieties and parabolic Higgs
bundles. The examples we construct admit a rather explicit description as
projective varieties obtained via Geometric Invariant Theory.
