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Thank you for your points Seesure. I suspect Person A might not be as promising as you suggest giving my last comment. I will have a look at MyHeritage thanks.

Thanks Flemming. To answer your questions
How would I be able to tell if these three people match each other?
Person A just states +21 and Person B +60 I have no indication of age for person C.
Person A has a small tree of 37 people, Person B a large tree of 570, and person C no tree. All three kits are managed by themselves.

Thank you both. To answer your comments first Ruskie. The mother and baby homes and the adoption boards no longer exist and all their records have been handed over to a state-run organization. We have met with this organization. They confirm they have details of both her parents. They claim that they have tried to contact her father on her behalf but have been unable to locate him. They claim that both his Christian and Surnames are very common which makes location difficult. They say they never had an address for him and are only aware of his name because that is the name my wife's mother gave them at the time of birth. They also suggested that her mother might have made up the name just to stop the Nun's from continuously asking. Although they claim they couldn't find this man or indeed confirm that he actually existed with this name they still refuse to give my wife his name claiming they can't under data protection legislation. We have spoken to lawyers who confirm that thgis indeed is the law in Ireland.
Thanks Flemming for your suggestions. I don't really understand DNA but I will have a look at what you have suggested.

My wife was adopted. A number of years ago she discovered who her mother was due to the adoption society making contact with the mother's family. But too late as her mother had died six months earlier. My wife subsequently got to know her half-siblings and her aunts and uncles but all claimed that they had no knowledge of who her father was. The aunts and uncles (ie her mother's siblings) have now all died and if they did know who the father was have taken this to their grave.
My wife has since taken an Ancestry DNA test and persuaded one of her half-sisters to do likewise and she has now eliminated all those people who they have in common so she is now left with a list that presumably are on her father's side. The problem is that the nearest match is fourth cousins. She has put the results on Gedmatch but to be honest neither of us really understand DNa. Has anyone any suggestions where to go from here?