A child always files a tax return in their own name for income earned from working. Sometimes if a child's only income is from investments, it can be reported on a parent's tax return. The child will not owe income tax if their income is less than $12,400, but they will owe self-employment tax (15% of net income after expenses).
Whether the child is your dependent depends on the usual tests, it doesn't specifically matter that you paid them. The tests are here.
https://www.irs.gov/pub/irs-pdf/p501.pdf
Very briefly, the 11 and 13 year olds are your dependents as long as they lived with you and did not provide more than half their financial support. The 19 year old is your dependent if was is a full time student for at least part of 5 months (such as the spring go his senior high school year), and he lived with you and did not provide more than half his support. If he was not a full time student, he is only your dependent if his total taxable income (from all sources) was less than $4300 and you provided more than half his support.
