I think Timber Hill are a subsidiary and they are trade execution, from my understanding no capital is actually held by them.
From memory all agreements I signed are with IB.
Yes TH are owned by IB. IB then in turn have an agreement for TH to act as principal. Your agreement would be with IB with some small clause in there for them to appoint an authority (typically Timber Hill). Which means that if TH stuff up, IB get to say 'not our fault, blame the principal' even though they own the principal. As I said I'm not sure if IB are still guilty of this, and they certainly aren't the only ones if they are. It has no impact on anything at all when things run well, it only becomes a big deal when things turn bad.