  We develop numerical tools and apply them to solve the relativistic
Yang--Mills--Higgs equations in a model where the SU(N) symmetry is
spontaneously broken to its center. In SU(2) and SU(3), we obtain the different
field profiles for infinite and finite center vortices, with endpoints at
external monopole sources. Exploration of parameter space permits the detection
of a region where the equations get Abelianized. Finally, a general
parametrization of the color structure of SU(2) fields leads us to a reference
point where an Abelian-like BPS bound is reconciled with N-ality.
