Just to be sure of what you're saying, does the math actually show a singularity to be of zero size, or just something vanishingly small?
As I understand it you can not say zero size. General relativity fails to make mathematical sense if you try to have zero size. However, it alone suggests zero size. This is a point where QM and GR have to be merged and until that is done the answer to this is: "Dunno".