I have booked a trip Man - Heathrow- Chicago - San Ant - Dallas -Heathrow- Man. A combination of First and C. The Dallas - Heathrow leg is with AA but booked under a BA number/ticket. I cannot assign a seat (C). BA says to contact AA and AA says that BA should have requested a seat for me at time of booking but did not, I am told that they are all booked but that one will be assigned the day of the flight. This does not fill me with confidence I will even have a seat in business let alone one can chose. Any advice please ?