The definition of their is a person or thing that belongs to or was made by them.(adjective)
See their in Webster's New World College Dictionary
possessive pronominal adjective
Origin: ME theyr < ON theirra, gen. pl. of the demonstrative pron. replacing ME here, OE hira: see they
See their in American Heritage Dictionary 4
adjective The possessive form of they.
Origin: Middle English
Origin: , from Old Norse theira, theirs; see to- in Indo-European roots.
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