In general, one parent cannot on his or her own give a child up for adoption. Giving a child up for adoption by both parents ends the financial commitment. If the child is with either of the legal parents, however, the other can be asked for support. I guess you do see some weird results, and it isn't all the same in every state. A lot of it is driven by economics, what the potential cost to the state is.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).