Not unless someone is going to adopt her or have a guardianship.
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California Family Code section 7822(a)(3) allows for termination of parental rights if the parent left the child without communication or support for one year and with the intent to abandon the child. No communication or support is presumptive evidence of abandonment. The presumption shifts the burden of going forward with evidence which means he would have to show why this was not abandonment. The requisite intent to abandon need not be permanent, only intent to abandon for a year. So you have a good chance, depending on his reasons for being gone.
Before you go through with the motion though, I hope you seriously consider all of the consequences. Your daughter would not have to just start sharing time with him. There would be a gradual period of introduction into her life. You would see whether he is serious about the commitment. Possibly a counselor would help with the re-introduction. If he follows through, your daughter will have a father in her life. AND you can make him pay support. You probably could use that help even though you have been making do without it. I don't know enough about your situation to cast a vote. I only hope you think it through and not act out of fear of the visitation plan. People that are strangers to your daughter now will some day be a very meaningful part of her life. Maybe he can be that. Or maybe he can't.
Both counsel are correct, Do you think he will be a good father? What about the child's need to know her father? Think about her future.
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Mr. Norton is correct, but even if the possibility exists the courts are loathe to terminate a parent's rights absent something blatant. With that being said you can protect yourself and your child by establishing a "reasonable" visitation schedule. It can start very conservatively, like supervised visitation for just a couple hours a week. That coupled with an appropriate support order may test test dad's true desire to be part of the child's life.