Tax Reform Update: Personal exemptions are suspended for tax years 2018-2025.
Per IRS Publication 17 Your Federal Income Tax (For Individuals), on page 26:
Tests To Be a Qualifying Child
Tests To Be a Qualifying Relative
If the child meets the rules to be a qualifying child of more than one person, only one person can actually treat the child as a qualifying child. See Qualifying Child of More Than One Person, later, to find out which person is the person entitled to claim the child as a qualifying child.
On page 33:
Relatives who don’t have to live with you. A person related to you in any of the following ways doesn't have to live with you all year as a member of your household to meet this test.
Any of these relationships that were established by marriage aren't ended by death or divorce.
Foster child. A foster child is an individual who is placed with you by an authorized placement agency or by judgment, decree, or other order of any court of competent jurisdiction.
See the IRS Who can I claim as a dependent? topic for more information.
Note that any link in the information above is updated each year automatically and will take you to the most recent version of the document at the time it is accessed.