  We study the limits of holonomy representations of complex projective
structures on a compact Riemann surface in the Morgan-Shalen compactification
of the character variety. We show that the dual R-trees of the quadratic
differentials associated to a divergent sequence of projective structures
determine the Morgan-Shalen limit points up to a natural folding operation. For
quadratic differentials with simple zeros, no folding is possible and the limit
of holonomy representations is isometric to the dual tree. We also derive an
estimate for the growth rate of the holonomy map in terms of a norm on the
space of quadratic differentials.
