No. Both parents have to give consent to a voluntary parental termination, so long as they are alive and of sound mind and reachable and that sort of thing. The only other type of parental termination would be an involuntary one based on abandonment (in Arizona, six months or more of non-payment of court-ordered child support and/or lack of contact), where of course the parent whose rights are to be terminated does not have to consent for it to happen anyway. Such an action can be brought by the state as well as the other parent and may go forward even without the consent of the other parent. Otherwise, when you're talking about a voluntary parental termination--which is what you are referring to--the non-terminated parent always has the right to weigh in on the subject. In sum, if you do not consent to the boy's father's parental rights being terminated, it will not happen, regardless of who if anyone might step in to take over the father's parental role. Even if the father's rights are terminated, you would still have parental rights over your son, and that would actually become an exclusive right; in other words, you would be the only holder of the right to determine how best to parent your child. Unless you were also to give up or lose your parental rights, no non-parent--grandparent or otherwise--is going to be able to sucessfully claim in loco parentis (step into the role of a parent due to some lack of parenting by one or both bio parents) and take over your parental rights. See also my Avvo legal guide on this same subject. Best of luck to you!