  The set of all possible spherically symmetric magnetic static
Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge
group $G$ was classified in two previous papers. Local analytic solutions near
the center and a black hole horizon as well as those that are analytic and
bounded near infinity were shown to exist. Some globally bounded solutions are
also known to exist because they can be obtained by embedding solutions for the
$G=SU(2)$ case which is well understood. Here we derive some asymptotic
properties of an arbitrary global solution, namely one that exists locally near
a radial value $r_{0}$, has positive mass $m(r)$ at $r_{0}$ and develops no
horizon for all $r>r_{0}$. The set of asymptotic values of the Yang-Mills
potential (in a suitable well defined gauge) is shown to be finite in the
so-called regular case, but may form a more complicated real variety for models
obtained from irregular rotation group actions.
