A problem with the R=U theory.

[Sir Bahamut]

You know, considering Ellone is the only little girl left in the town....
So maybe the other little girls are killed or captured then rejected and disposed of.

Well, even if we assume Ellone was the only girl left, there are other towns in the world of FF8 with many more little girls. Why do we see none of them? Although there's bound to be other potential sorceresses elsewhere in the world, Adel specifically goes for Ellone alone.

That is after Odine researched her and Adel came to know her power, right?

Depends. If you assume Ultimecia was possessing Adel, then she knew of her power before Odine did his research. If not, then your explanation can fit.

Maybe I will answer this myself. Ultimecia has the junction machine Ellone so she can send her consious to the past so she just went back to 10 years later after Adel's event and possess Edea. But this dun make sense too since why will she do such a meaningless thing?

This is only a problem depending on what view you have on time in FF8.
If you believe you can change the past, then this makes no sense. After all, Ultimecia could have gone back and possessed Adel again before she was sealed up, except this time she'd know that they would be trying to fool her, so she could easily change things so she didn't get sealed up, enabling her to keep on doing research on Ellone. One possible solution to this could be that she didn't want to wait around for Ellones powers to awaken within her, soe she figured she'd look for her when she was more grown up.

If you however believe you can't change the past, then there would be no gap inbetween these two events. Immediately after Adel was sealed up, Ultimecia'd jump to Edea, and that'd be that.

But also in that scenario you might ask why she doesn't go back and try and change things(assuming that Ultimecia doesn't realise that you can't change the past). One possible answer is that possessing Adel again would result in Adel having not one, but TWO Ultimecias inside her! Perhaps this would be too much of a strain.

I'm not sure though...