  We use a renormalisation group based smoothing to address two questions
related to Abelian dominance. Smoothing enables us to extract the Abelian
heavy-quark potential from time-like Wilson loops on Polyakov gauge projected
configurations. We obtained a very small string tension which is inconsistent
with the string tension extracted from Polyakov loop correlators. This shows
that the Polyakov gauge projected Abelian configurations do not have a
consistent physical meaning. We also apply the smoothing on SU(2)
configurations to test how sensitive Abelian dominance in the maximal Abelian
gauge is to the short distance fluctuations. We find that on smoothed SU(2)
configurations the Abelian string tension was about 30% smaller than the SU(2)
string tension which was unaffected by smoothing. This suggests that the
approximate Abelian dominance found with the Wilson action is probably an
accident and it has no fundamental physical relevance.
