  The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and
axially symmetric case to a harmonic map with prescribed singularities
$\p\colon\R^3\sm\Sigma\to\H^{k+1}_\C$ into the $(k+1)$-dimensional complex
hyperbolic space. In this paper, we prove the existence and uniqueness of
harmonic maps with prescribed singularities $\p\colon\R^n\sm\Sigma\to\H$, where
$\Sigma$ is an unbounded smooth closed submanifold of $\R^n$ of codimension at
least $2$, and $\H$ is a real, complex, or quaternionic hyperbolic space. As a
corollary, we prove the existence of solutions to the reduced stationary and
axially symmetric Einstein/Abelian-Yang-Mills Equations.
