Possibly worth checking the archive on this. I've found at least one thread: related discussion: I have a dog bzw. I have got a dog

I got a brother = colloquial; in "formal" language it would mean you've received a brother (as in: your mom just gave birth to a boy)

The difference between "have" and "have got" is negligible in AE (for the most part).

I have got a brother is simple present, not present perfect simple (despite the "have").
Both sentences mean the same.
The difference comes with the question and the negative.
He has a brother. Does he have a brother? He doesn't have a brother.
(Has he a brother? and He hasn't a brother are theoretically possible, but they sound very odd.)
He has got a brother. Has he got a brother? He hasn't got a brother.

thank you all for your answers but I am still not sure - sorry!
Could I say in general:
For possession I can use either "have" or "have got" (Present simple) but to express possession in all other tenses I can only use "have"?
Sorry for bothering you !

"In general", yes - although it's not quite as simple as that. (It never is.)

Thank you tomtom!!!

Not in AE. For example, "he had" has a different meaning than "he had gotten" (and "he had got" isn't even used).

No, it's not the same, at least not in "proper" grammar.

You say "got" when you own something, or when you have a disease, and so on.

I've got a car, I've got a bad cough.

But you don't own your family, so it's

I have a brother.

But native speakers, particularly in British English, often ignore this rules, so it depends on whether you want to be absolutely correct, or go with the flow.

That sounds a bit nit-picky to me, Mini Cooper.
I have got a Mini = I actually own the car.
I have a Mini = I have hired / stolen the car.
????

tom tom - it's very nit-picky, which is probably why it's (quite rightly, imo) so often ignored. I got it from a book - Business English Grammar by Paul Emerson (Grammar Guru).
It's also very British. Americans tend to laugh at us when we say "got", at least all the Americans I know are always pulling my leg when I use is.

By the way, I've got a Mini, too.
I have a nice time driving it.

As for AE: I've got you, babe. :-)

dude - I've got you to understand! Lovely! (Or "terrific" as you would no doubt say.)

That would be wrong, though, Mini. It should be "I got you to understand." Then it would be awesome! ;-)

Awesome is an awesome word, dude!