Can a unwed mother will her kids to her boyfriend upon her death if they are not his kids but another guys?

This is a tough situation.  First, if your girlfriend has a legal custody agreement with the children's father, that agreement would likely spell out who obtains legal and physical custody if one of them passes away.     She can certainly appoint a guardian for her children in a legal document, so long as any custody agreement doesn't prevent this.  Her wishes could then be considered if she passed away and someone needed to petition the probate court to appoint a guardian.  There are many factors that go into making this determination.