Sets of approximation and interpolation in ℂ for manifold-valued maps

We give examples of non-smooth sets in the complex plane with the property that every holomorphic map continuous to the boundary from these sets into any complex manifold may be uniformly approximated by maps holomorphic in some neighborhood of the set (Mergelyan-type approximation for manifold-valued maps.) Similar results are proved for sections of complex-valued holomorphic submersions from complex manifolds.