| First it is nice you want to help but at times some things are not possible.
I guess if you had enough money you post a copy of the photo in major newspapers and see if anyone knows them. But in this case, the man most likely does not even know he has a child, so he is not looking.
And if the mother does not even know his last name it was obviously not a seroius or long term relatinship
So unless the mother has some more info, there may be little you can do |