On the U.S. Customs and Border Patrol web site, there is the following notification:
Traveling with Children
When U.S. citizen children under the age of 16 arrive by land or sea from Canada or Mexico they may present an original or copy of their birth certificate, a Consular Report of Birth Abroad, or a Naturalization Certificate.
Unless the child is accompanied by both parents, the child must have a notarized letter from the other parent or signed by both parents stating, "I acknowledge that my son/daughter is traveling outside the country with [the name of the adult] with my permission."
Groups of Children: U.S. citizen children under the age of 19 arriving by land or sea from Canada or Mexico and traveling with a school group, religious group, social or cultural organization or sports team, may present an original or copy of their birth certificate, a Consular Report of Birth Abroad, or a Naturalization Certificate. The group should have a letter on organizational letterhead with:
The name of the group and supervising adult(s). The names of the children on the trip and their primary address, phone number, date and place of birth, and name of at least one parent or legal guardian for each child. A written and signed statement of the supervising adult certifying that he or she has parental or legal guardian consent for each child.
This requirement seems only to apply to U.S. children coming into the U.S. from Canada or Mexico, but not any other country, and only by land or sea, not air. Is that right? It's kind of ambiguous because it is not clear whether the Canada/Mexico qualification only applies to the first paragraph or to all the paragraphs.
In other words, let's say I am flying from the U.K. into the United States, do I need to have both parent's notarized permission to bring a U.S. child with me?