  We introduce a new variant of the coarse Baum-Connes conjecture designed to
tackle coarsely disconnected metric spaces called the boundary coarse
Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected
spaces that are known to be counterexamples to the coarse Baum-Connes
conjecture. In particular, we give a geometric proof of this conjecture for
spaces of graphs that have large girth and bounded vertex degree. We then
connect the boundary conjecture to the coarse Baum-Connes conjecture using
homological methods, which allows us to exhibit all the current uniformly
discrete counterexamples to the coarse Baum-Connes conjecture in an elementary
way.
