US Customs and Border Protection (CBP) strongly recommends that if a child is travelling to the US with one parent, the travelling adult should have an acknowledgement from the child's other parent. Alternatively, in the case of a child traveling with grandparents, uncles, aunts, sisters, brothers, friends or in groups*, the travelling party should have a similar acknowledgement signed by both parents stating the following:

"I acknowledge that my wife/husband/etc. is travelling out of the country with my son/daughter/group. He/She/They has/have my permission to do so." 

If there is no second parent with legal claims to the child (deceased, sole custody, etc.),  any other relevant paperwork such as a court decision, birth certificate naming only one parent, death certificate etc. will suffice. CBP also suggests that this be notarized.

While CBP may not ask to see this authorisation at each visit, if the passenger does not have this, they may be detained until the circumstances of the child traveling without both parents can be fully assessed.

Adults travelling with children should also be aware that while the U.S. does not require this documentation, failure to produce notarized permission letters and/or birth certificates could result in travellers being refused entry. This rule will also apply for school groups, teen tours, and vacation groups.