Assuming by some sleight of chance Sealion is successful, what happens to Britain's empire?

Okay, okay, to clear some misconceptions... I'm quite aware Sealion is the poster-child for "unlikely" on this board. And personally I don't think it's very plausible either. But let's assume it goes through - an earlier 1930s POD's butterflies leads to Germany developing a better airforce and navy (esp. transports), while Britain has rougher political leadership.

Germany takes over Great Britain. I assume, like France, they set up a puppet regime. (Were there any plans for governing Britain, anyway?) What happens to the colonies? I know the Dominions would (probably) fight on, but what of colonially-governed provinces/crown colonies like, say, Nigeria or Egypt, close in Africa or what?
Hitler didn't want to destroy the British Empire, but I he'd want a friendly administration. I don't think he'd take a lot of territory from the British though.