  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 behavior of the surfaces is based on the asymptotics of Delaunay-type
surfaces, i.e., rotational symmetric minimal cylinders. The minimal surfaces in
$\mathrm{H}^3$ extend to Willmore surfaces in the conformal 3-sphere
$\mathrm{S}^3=\mathrm{H}^3\cup\mathrm{S}^2\cup\mathrm{H}^3$.
