1. They're=They are: The PRONOUN they and the VERB are.
Example: They're (They are) coming over today.
2. Their is a possessive pronoun which shows OWNERSHIP of something.
Example: Their dog is sick.
3. There is a location which indicates WHERE something is.
Examples: There is a man looking for you.
The car is over there.
If the word there's is used, it's only to combine the words 'there and is' never to imply that someone is possessing something. In other words, there's never takes the place of the theirs.
For example,
The room is theirs. Note: No apostrophe is needed.

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Spell Check Anyone????
Non-FictionMATURE PEOPLE WANT TO READ MATURE BOOKS WITH CORRECT CONVENTIONS: SPELLING AND GRAMMAR. If you want to publish, please take the spelling and grammar seriously. No one wants to buy a book filled with mistakes. I have requested refunds because if I am...