Can I receive earned income credit even if my ex claims all three kids every year, but they live with me 50%?

You may qualify for the Earned Income Credit even if you don't claim your children as dependents on your tax return. Your children must meet all of the requirements to be a qualifying child for the credit. To qualify, your child must:

• Be your child (including legally adopted), stepchild, foster child, sibling, half-sibling, step-sibling, or a descendant of any of them (for example, your grandchild or niece); and
• Be permanently and totally disabled OR under the age of 19 as of December 31, 2015 (under 24 if a full-time student) and younger than you (or your spouse, if filing jointly); and
• Have lived with you (or your spouse, if filing jointly) for more than half the year; and
• Not file jointly with their spouse unless they weren't required to file but did so anyway to claim a tax refund; and
• Have a valid Social Security Number (not an ITIN).

TurboTax will automatically walk you through the process when you add the dependent on the tax return as long as you are the custodial parent (the child lived with for more than half of the year). If your child lived with you for more than half of the year, and you indicate that in the personal information section, then you will have the option to claim your child as a non-dependent for EIC and that the other parent is claiming the child as a dependent.

https://ttlc.intuit.com/replies/3299933