This is my computer not their computer, they're intending to take it with them so there will be no computer left here.
i think it is easy -their-
Their: is possesive pronoun, you use it when you want to say that something belongs to a group of people in which you are not included.
Ex: Their house is the one at the corner.
There: this is an adverb, you use it when you want to point out a thing. You use it if you want tell somebody where something or somebody is.
Ex: There is the pen.
They're: this is the contraction of "They Are".
Hope this helps! ..
Their is a possessive pronoun.
They're is a subject pronoun plus a contracted verb.
There can be an adverb of place or a noun of location.
I absolutely agree with Mihai_alexandru
I keep seeing this being done wrong, by supposed natural English speakers as well. If they stopped to think what they're trying to say, would they get it right?
their - something that belongs to them
there - referring to a place, answer to where
they're - short for they are
The correct answer is "their"