This Q&A addresses the underlying Catholic principles of your query.
This article addresses some of the non-Western cultural conflicts that arise when Catholicism is embraced by traditional polygamists. I'm sure it's nothing new, and the situations and beliefs were probably well understood in ancient cultures that had Christian converts.
The long and short of it is that marriage, not just in Catholic tradition, but also as a matter of normative cultural practice in Western Culture (Europe, the Americas, Australasia, etc. whose civil culture owes its sense of justice, ethics and morality to Catholicism) is one woman and one man. Some countries uphold polygamy as a matter of culture, civil law and ancient custom. Notably in Africa.
That being said, a Pagan man who has three "wives" married according to his Pagan custom, will discover during the process of conversion that he really only has one wife and two extramarital sex partners. So, he's going to be in a little bit of a pickle.
Ultimately, I think he'd have to be educated as to what Christian marriage really entails, ideally before conversion so that he and his "wives" all understand what's going to happen. He'd probably have to accept that only one of his wives is actually his true wife. Most likely, this would be the one he married first. This is because the Church recognises the validity of "natural marriage", a non-sacramental marriage that occurs between two non-Christians basically. Whether a marriage is natural or sacramental, the Church teaches that you only get one shot. Unless the spouse dies.
I can't find anything specific as to what would happen to the other two women. Since they never had valid marriages, and if they converted as well, they'd certainly be free to marry in the Church if they desired.
The matter of all the children. Since marriage doesn't dictate the nature of the role of fatherhood, our man would still bear full responsibility for the care, raising, educating and role modelling of Christian manhood to all his children equally. His situation would be no different than any other man who engages in serial monogamy via divorce. There is no such thing as "legitimate" and "illegitimate" children in Catholic teaching, so all the children are of equal dignity in that regard.
Practically speaking, I'd argue that a sensible, pastoral, common sense approach would be for the three adults to seriously discuss the situation. Perhaps a viable solution would be for the man and his legitimate wife to live together as spouses with their own kids, and for the two former wives to live either together or separately in close proximity but in a separate house. This would keep the whole extended family together as much as possible and would allow for the kids to be with both their father and their mother. I offer this kind of ideal solution simply because I would hope that the man actually has gained some true affection for all the mothers of his children and that he has in some way chosen to love each of them. They certainly don't deserve to be thrown away with the rubbish after the conversion party!
That would require a lot of commitment and self-sacrifice on the parts of all four parents.