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According to Etihad's website on this subject, once you clear US Customs and immigrations for the US at Abu Dhabi airport, there is no need for further checks when you arrive in the US.
US Customs and Border Protection (CBP) facility in Abu Dhabi
The United States Customs and Border Protection (CBP) facility at Terminal 3 (T3) in Abu Dhabi Airport is a purpose-built facility that allows US bound passengers to process all immigration, customs and agriculture inspections in Abu Dhabi, before you depart. It is the only CBP facility in the Middle East, and one of only a few outside of North America.
After you have cleared customs and immigrations for the US at Abu Dhabi airport, there is no need for further checks when you arrive in the US. You can even check your baggage through to your final destination in the US.
Itβs the fastest way to get through the airport and on to your final destination in the US β your way.