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Thank you for using justanswer. As long as your children do not provide more than 50% of their own support (including wages, investments, etc), they are under age 19, and live with you more than half the year, then you may still claim them under the Qualifying Child rules, and it sounds like you will have no trouble meeting the requirments.
If your children have any Federal tax withheld, and want to file to get that withholding back, then they would file a Form 1040EZ, marking the box that states they were being claimed by somebody else (you, the parent) and they would still be able to recover most, if not all, of their Federal tax withholding.
They will not be able to recover their social security or medicare tax withheld until they retire, just like the rest of us. (Sometimes first time filers think they can get everything back, so thought I'd mention that one)
I hope this helps.
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