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1. As long as you continue to meet the tests for claiming dependents, the children are your dependents....your exemptions.
As the children have their own taxable income, you would file their tax returns to report their income and pay their taxes.
2. If you provided more than half their support for the year, then you meet the support test. Total support includes amounts spent to provide food, lodging, clothing, education, medical and dental care, recreation, transportation, and similar necessities.
You determine whether you have provided more than half of a person's total support by comparing the amount you contributed to that person's support with the entire amount of support that person received from all sources.
This includes support the person provided from his or her own funds. A person's own funds are not support unless they are actually spent for support. For example, if you saved their support in a separate account for them, then it would not be counted as funds provided by them for their support.
http://www.irs.gov/pub/irs-pdf/p501.pdf (Exemptions,Standard Deductions,and Filing Information)
As you have no doubt always done, your children have been claimed as your exemptions on your return since they are your dependents. The fact that they might file tax returns for their independent sources of income does not alter this.
A review of the above Publication 501 will provide you with ample information on this area. It will answer questions that you may not have thought of asking yet.
A key to remember is that your children cannot claim an exemption on their own tax returns if you claim them on your tax return.
Hopefully, I have addressed your question in full, but please do contact me if you have additional thoughts.