  We construct a semi-stable formal model of a wide open rigid curve with a
semi-stable covering, and study the l-adic cohomology of the rigid curve. We
describe the l-adic cohomology of the rigid curve using the l-adic cohomology
of the irreducible components of a semi-stable reduction, and homology and
cohomology of some graphs. We also prove the functoriality of the description
for a finite flat morphism that is compatible with semi-stable coverings of
wide open rigid curves.
