Thank you @Richard for bringing this topic here because most of the English learners get confused by the different usage of "Get", especially the one you mentioned i.e, "got" and "gotten". But after reading the crystal clear explanation of @Su.Ki., I think I'm a bit confident to use it accordingly without being confused.

I agree with you @Richard that Su.Ki. is the titan in explaining any doubts related to English in a simpler and clearer way. Thank you, @Su.Ki. and @Richard for your contribution to this language hub:)

Dear Su.Ki.

First, let me say how very grateful I am for your comments, explanations and advice.
All of your comments and explanations on italki are so very clear, orderly and helpful.
You certainly possess an innate skill, the art of clarity. I envy (in the nicest way :) your skill.

Now, with respect to my discussion:

- I should have taken a little more time to clearly state my case. I did not mean that 'have got' posed a grammatical problem for me; simply that I prefered the sound of 'have gotten' over 'have got'.

- I agree completely with your first usage explanation, i.e., the use of 'got or gotten' as the main verb.

- Yes, in Canada we use both American and British spellings, however, I am not so very sure that our grammar is entirely American (and frankly, I hope that is not the case). When I was in school (50s, 60s, and early 70s, we were taught British English spellings and grammar). Now, I'm not sure what the young people are learning, except to say that their spelling skills have gotten worse due the texting phenomenon.

- Your second explanation of the use of got also poses no problem for me, and of course I concur with your explanation.

- For some unknown reason (other than accounting for my horrific understanding of English grammar :) I've always thought that the more sophisticated-sounding 'gotten' was British in origin, and I've always prefered the sound of the -en form. Oh well, now I know better.

In conclusion, I truly appreciate the time and effort you put in to writing your most-excellent clarifications of the two usages. I am sure that all English learners benefit from your good work. In fact, I would be one of the first people to download a free, illegal, scanned copy of any grammar publication authored by you. Truth be told, if you published a book, similar to Michael Swan's Practical English Usage, I'd surely pay full price for it and treasure it.

Thank you again Su.Ki. 

Sudeep...

Thank you for your support and your kind comments and appreciation for Su.Ki.'s clear professional explanations and help.

Since joining italki you have consistently and graciously expressed your gratitude for the efforts of several members.
Your generous comments are very meaningful and rewarding to those of us who contribute to these discussions... thank you Sudeep, you are truly a gentleman.

2.  Now consider these sentences:

I haven't got any time.

He's got three older sisters.

It's late. We've got to go.

Does the use of 'got' make you uncomfortable here? It shouldn't do. Although the structure of these sentences looks identical to the present perfect sentences in the section above, they aren't actually present perfect sentences at all.  In the sentences in the first section, have is just the auxiliary verb and gotten or got is the past participle of the main verb. They describe an action in the past which has an impact on the present. In contrast, the sentences in this section are actually in the present tense, and refer exclusively to present time. Here, have is the main verb (indicating possession of some kind) and got is ....well, nothing at all, really. When we contract the main verb to just s or  ve, we need the got as kind of stabiliser, to balance the sentence and avoid ambiguity. ( 'He has three sisters' is hard to say in fast speech and 'He's three sisters' might be confusing). Got carries no meaning in these sentences, so you needn't worry that it isn't a 'correct' past participle. It's just there as a little helping word.

Just think of 'He's got three sisters' and 'We've got to go' as an idiomatic form, used mainly in informal speech. It doesn't necessarily follow the strict rules of grammar, and has no parallels with other constructions. Accept it as it is. It's a perfectly correct idiomatic form, and it's appropriate for any situation other than formal contexts. No need to feel uncomfortable.