"have" vs."have got" in American and British English

To my BrE ears, ‘I have got a cat’ sounds like a full sentence, whereas ‘I have a cat’ sounds like a lead-in to a fact about that cat, such as if it were followed with, ‘who chases her own tail!’ It also sounds like the person has several cats, but is only talking about one of them.

Do bear in mind most people will use the contraction I've got in speech, and it does sound more informal than I have.

You are correct about the negative and interrogative too:

• I have not got a cat, vs.

• I do not have a cat

   

• Have you got a cat? vs.
• Do you have a cat?

Besides its "primary" verbal meaning (possession), "have" is used as a verb of necessity, as a near-synonym of "must".

• I must go.

• I have to go.

• I have got to go.

This last form - "have got to" - is very often shortened to "gotta", and I suspect that this may be a large part of the reason why Americans regard the "have got" construction as less formal.

• When ya gotta go, ya gotta go!

• Gotta dance!

This not a matter of what's more formal or more proper or more anything. This is a very complex subject, with a number of constructions, and rules, and idioms, and complications involved. The presenting question covers one small tip of the iceberg; this answer covers the iceberg. Oh, and this discussion is about American English; I take no responsibility for UK usages.

First, the verb get has two basic meanings, both grammatical rather than lexical
(in the following, "causative/inchoative" means 'come to be/become/cause to become'):

• get can be the causative/inchoative of the auxiliary verb have, in all its uses
  She has/She got leprosy. She has/She got a car. I had it done/I got it done.
  = She came to have leprosy. She came to have a new car. I came to have it done.

• get can also be the causative/inchoative of the auxiliary verb be, in all its uses
  She was/got married by a priest. He was/got going fast on the hill. They were/got tired.
  = She came to be/became married. He came to be going fast. They came to be tired.

Second, the present perfect construction uses the auxiliary have, and occurs in its Stative/Resultative Perfect sense with 'come to have' get ; in two variants: have got and have gotten. We only deal with American usage of have got here.

Third, since get means come to have, and since this is Stative/Resultative perfect, has got means 'has come to have'. OK, except that if one has come to have something in this sense of the Perfect, it must be true in the present that one still has it. So

• I've got a car = I have come to have a car = I have acquired a car = I have a car.

which immediately confuses the have of the perfect with the have of possession.

Fourth, auxiliary verbs like be and have are almost always contracted (they're auxiliaries and have no meaning; they're particles, intended to direct your attention, not to hold it). This means they're reduced to final consonants cliticized to subject NPs, mostly pronouns.

• I've, I'm, I'd, You've, You're, You'd, It's, It'd, We're, We've, We'd, They've, They're, They'd

Fifth, these clitics in turn get deleted whenever possible. After all, we already can't tell the difference between the contraction she is and she has, or between we would and we had, and that doesn't bother us. Plus, English does not prefer initial clusters with /ɡ/, like /zɡ vɡ dɡ/, so /z v d/ are lost most of the time before got.

• You've got the answer -> You got the answer.
• I've got the answer -> I got the answer.
• He's got the answer -> He got the answer (reified by children to He gots the answer.)

Finally, since have is more often used as an auxiliary than to mean possession, and since the have got construction means the possession sense of have, it has come to take over the possession sense of have.

This is syntax in action, still changing, different now from the way it was 50 years ago, and coming to have new senses and new uses and new distinctions every day. It's alive, after all.

Just to make sure I have the question right - it is:

When is it appropriate to use "have a.." or "have got a..." for possession in British and American English?

Writing

Maybe if we start with something we can all agree on: it's generally not appropriate to use "have got", let alone abbreviated forms, in formal written English, whether in Britain or America. "I have got a degree in Maths from the University of Bath" doesn't sound right for a written job application; "I have a degree..." sounds better.

So the difficult question is especially about spoken English in different contexts and then summarising this in a way that beginner to intermediate level EFL students can actually understand.

Speaking in Britain

The fact that "have got" and abbreviated forms are not common in written English is a clue about formality: "I have an idea" is slightly more formal then "I've got an idea".

But this doesn't change the fact that it is appropriate, in most circumstances, to use either "have" or "have got" (abbreviated: people say "I've got" not "I have got" unless they're empahacising something they have compared to something they don't) but in most contexts "have got" is more common. In summary, for most students in doesn't matter which form they use for spoken British English. See these corpus results for have+idea vs. 've got+idea, which display similar numbers of results and little difference in context.

I'd also argue that in spoken English pronunciation of either form is more important than the choice of form per se.

Speaking in America

I'm British so not best placed to comment here. It seems the consensus on ESE and from what I see online is that American English prefers "have" to "have got". My opinion again is that it doesn't matter a lot for most EFL students which form they use since both exist in most spoken contexts but since "have" is more common it is more appropriate.

I also had a go at an ngram but it didn't really help much :-)

'Have you got time?' is informal in USA. 'Do you have time?' Is formal in the USA. USA uses 'got' in this way: as an emphases or as a repetition.

E.g.: "I have got to get a cat.' 'Got' is a repetition of get, thus creating an emphatic statement. Otherwise, got is not much used in the USA.

There used to be a distinction. "Do you have a car?" meant "Do you possess a car", whether the car is here now or at a garage or parked in your driveway at home. "Have you got a car?" had a more immediate meaning of "Have you got it with you now?"

However, I think that distinction disappeared a long time ago.

I agree that in the US 'have got' would be more informal than 'have' in the sense of possession. Not by much, however. Not at all, in the sense of obligation.

But what has me tearing out what's left of my hair is the repeated suggestion that Americans avoid 'have got.' I've lived my whole life in the Southern US and I use it all the time, as does (I think) everyone else. For example, the usual colloquial way of asking to borrow someone's cigarette lighter is "Got a light?" not "Do you have a light?" Of course, 'have' is also used very often.

It seems that "have" and "got" have the same meaning in this context, making the "got" in "have got" redundant and unnecessary. It doesn't seem to add any significant emphasis or meaning. It is probably used as a matter of habit or perhaps as a better sounding phrase to a certain cultural ear. I picked up the phrase "got to get going" by way of my mother who was from the Texas panhandle. This always sounded right and a bit melodic to my ear just from hearing it so often. When I traveled to other parts of the states or out of country, the phase was always found to be funny and excessive. Sometimes it is just local custom that dictates such things.