Definition of "their" [their]

• Used as a modifier before a noun: their accomplishments; their home town. (adjective)
• Usage Problem His, her, or its: "It is fatal for anyone who writes to think of their sex” ( Virginia Woolf). See Usage Notes at he1, they. (adjective)

American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

• "Companies such as Google, Walmart, eBay, and FedEx are already using larger stacks of the blocks at their facilities in California, where state and federal tax credits for alternative-energy systems defray their  steep cost."
• " The creature kingdom was sure of their cause and resolute in their determination to become free from the despoilment by the beasts of theupright worms:  their canine accomplices."
• "BUT -- even Clinton supporters will, in their hearts, have to admit that if * their* candidate had the majority of pledged delegates, superdelegates, total delegates, contests won and Obmaa had a 0.5% lead in the popular vote, they would truly go nuclear if someone argued that because of that he should be the nominee."