No limit for the child tax credit. The limiting factor is your tax liability which the credit lowers, but only until it reaches zero. The credit is $1,000 peer child, but if you only have a tax liability of $1,500, for example, then that would be all would get. However, you might qualify for the additional child tax credit if your income is within certain limits.
For the EIC the maximum is three qualifying children dependents.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**