We construct minimal surfaces in hyperbolic and anti-de Sitter 3-space with the topology of a n-punctured sphere by loop group factorization methods. The end behaviour of the surfaces is based on the asymptotics of Delaunay-type surfaces, i.e. rotational symmetric minimal cylinders. The minimal surfaces in H-3 extend to Willmore surfaces in the conformal 3-sphere S-3 = H-3 boolean OR S-2 boolean OR H-3.