The United States of America. Being the freest and best country in the world it is logical US takes superior democracy to all regions in the world.
The people who have lived there and worked the land for generations. Who they want as their sovereign country, if any, should be their choice.
If you acquaint yourself with the full history , the sagas are quite amazing for such a small group of islands . Frankly , I think any independent and objective investigator would find it very hard to provide a convincing case for Argentinian sovereignty . Spain holds a far greater claim , but , regardless , the full story going back about six hundred years has endless twists and turns . Perhaps renaming them Thatcher Islands would spark a first rate spat and we could have the pleasure of flexing ourselves again . Let's face it , we don't want to be messing with anybody too big .
It really hardly matters, as the status quo will continue uninterrupted, save for the occasional squawk from Argentina when it gets into political difficulty, or thinks there might be something to be had (like oil). The Argentinians know their military would be no match for the UK's in a declared war, and an invasion of the islands is now incomparably more difficult than it was in 1982. They also know that most EU nations would side with Britain over the issue (the Falklands are listed as British territories with the UN, and accepted as part of the UK by the EU). For Britain's part, she has enough domestic problems to dissuade her from engaging in further unnecessary conflicts, if it can possibly be avoided. So only an invasion of the islands by the Argentinians would prompt a military response from the UK - and that is highly unlikely.