I am flying into LAX on an American Airlines flight from LHR, so presumably I will arrive at the TBIT international terminal (although American doesn't seem to be listed on the terminal maps for TBIT)? I assume I will clear customs and immigration there (like every other American airport), and will end up landside. I am then connecting onto an American domestic flight. Will this be from Terminal 4? How do I get there? Is there a landside bus or train service? Both the American Airlines and LAX websites seem a bit weak at explaining this.
According to the LAX map on aa.com - all American Airlines (and American Eagle) flights use Terminal 4:
Therefore, I do not see an issue during transit.
I did a cursory check on AA international flights arriving in LAX I found AA216 from Sau Paulo, and it also arrived at Terminal 4.
It seem TBIT is for international airlines and not international flights.
United Airlines, Delta Airlines and American Airlines all have their own immigration and customs facilities within their repsective terminals. You will clear formalities and connect with your domestic flight in the same terminal.
TBIT is ueed primaily by international carriers with a limited presence in LAX (ie only one or two flights). International airlines with multiple flights often share a terminal with their alliance's US member to make connections easier.
Having done this now, I can say that the answer I'd previously accepted (Terminal 4) was incorrect. The flight I was on (an American Airlines one) landed at TBIT. It was fairly easy to "transfer" to Terminal 4 though - after re-dropping my bag, it was just a short walk outside - fairly obvious once you've looked a terminal map.