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Quote susan53

1a. (On the phone) A : Can I speak to John ? B : Can you phone back later? He's just got into the bath.
1b. When I saw David he had just got back from Australia.

I'd say 'gotten' for both.

Quote susan53

2a. Luigi's English has got a lot better recently.
2b. The tests showed that her eyesight had got considerably worse since the previous check-up.

again 'gotten' for both.

Quote susan53

3a. Hey everybody! I've got my exam results!
3b. When I saw John, he had just got his exam results.

The first one, I'd say 'got' to mean 'possess' or 'gotten' to mean 'received'
The second one, I'd use 'gotten'

Quote susan53

4a. Look! I've got a new car.
4b. He said he had got a new car.

I'd say 'got' and 'gotten' for these two, respectively

Quote susan53

5a. I've got a headache.
5b. I've got two sisters.
5c. I've got red hair

all 'got'

Please don't ask why
but maybe as a general rule I say 'have got' to mean 'possess' and 'have gotten' to mean 'have received'