Are the ones that tested negative. But if none of the names turn out to be Joseph Smith's children, isn't that just as bad? Polygamy's entire stated purpose was to raise up a righteous seed to the Lord and yet it didn't work. If the Lord gave these women to Joseph to produce offspring with, why didn't that happen? God is certainly capable of seeing that someone he wants pregnant gets pregnant. If polygamy wasn't to give Joseph children, then it must have been to give Joseph sex toys. Seriously. There are two reasons to marry these women: children and/or sex. God didn't send children.
If Joseph was supposed to "raise up seed" he did a pretty lousy job, and if he married these women to simply create "loose dynastic ties" (whatever the h*ll apologists mean by that)without progeny, he was going against God's plan by NOT "raising up seed". And why was he marrying other men's wives, and why would God allow so many of his confirmed children to die. That's not even mentioning the whole Dr. Bennett and his reported abortion services. Sorry to veer OT, but--it's all enough to make a TBM's head explode......
When Josephine Rosetta Lyon's mother was dying, she told Josephine that she was Joseph Smith's child. Even if they currently haven't found any living relatives of children fathered by Smith, this is still a confession that she had sexual relations with him. That disputes the argument that they were spiritual wives only.
It looks like a lot of the suspected children fathered by Smith also died in infancy, like many of Emma's children did.