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I agree that this article does not describe clearly how the method works. Obviously one can sequence (or haplotype targetted regions) of both parents independently, and presumably the fetal DNA from the mothers plasma--though what would be sequenced would be a mixture of the mothers + fetal DNA, and so this would only allow identification of which paternal alleles/haplotypes had been inherited by the fetus, not which maternal one--ie. it would remain ambiguous as far as I can see.