For which countable group G, does the moduli space X(G) = Aut(G) Hom(G,PSL(2,R)) / Inn(PSL(2,R)) contain (uncountably many distinct equivalence classes of) dense faithful representations? Groups with such properties are called flexible. We prove combination theorems for flexible groups, and show that most Fuchsian groups and all limit groups (possibly with torsion) are flexible. The diversity of quasi-morphisms on those groups will follow. Implications for word-hyperbolic groups and mapping class groups will also be discussed. Joint with Thomas Koberda and Mahan Mj.