01. A guy who isn't your boyfriend, or your husband, or even really your friend, but happens to be the father of your child.
02. Your boyfriend/husband, who you have a child with, but who
ran out, or doesn't come by, or never pays for what the baby needs, so you don't want to call him a husband/boyfriend/father.
03. Can also be used negatively, to insult the supposed father of your child.