  We have studied the monopole-percolation phenomenon in the four dimensional
Abelian theory that contains compact U(1) gauge fields coupled to unitary norm
Higgs fields. We have determined the location of the percolation transition
line in the plane $(\beta_g, \beta_H)$. This line overlaps the confined-Coulomb
and the confined-Higgs phase transition lines, originated by a
monopole-condensation mechanism, but continues away from the end-point where
this phase transition line stops. In addition, we have determined the critical
exponents of the monopole percolation transition away from the phase transition
lines. We have performed the finite size scaling in terms of the monopole
density instead of the coupling, because the density seems to be the natural
parameter when dealing with percolation phenomena.
