Comment: But the question is

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In reply to comment: Children are children and are (see in situ)

But the question is

what happens when the children grow up and become adults if their parents have voluntarily placed the family under some form of government? When the children grow up they find themselves governed by rules they never consented to, and yet practically speaking there may not be a realistic option for them to disassociate themselves from the system they were born into.

What is their status, from an AnCap point of view? If you say that they cannot be forcibly expelled from the society in which they were born, but cannot be held to regulations that their parents voluntarily agreed to but that they the children did not consent to, then you have one set of problems. If you say that the parents were able to make those commitments on behalf of their minor children, in such a way that the children remain bound by those commitments without consent as adults (subject to whatever mechanisms, if any, are provided for changing their situation) then you have a different set of problems.