  We prove the rational HK-conjecture for a large class of transformation
groupoids in the case when the relevant action has torsion-free stabilizers. A
revised version of the rational HK-conjecture in the case of (possibly) torsion
stabilizers is introduced and proved for a large class of transformation
groupoids. In particular, this revised version holds for Scarparo's
counterexamples to the original rational HK-conjecture. The key tools used are
the Baum-Connes conjecture and a Chern character defined by Raven.
