The short answer is that you will need to apply to appointed the guardian of each child's person and estate. The long answer is much more complicated. The kids' fathers have a default right to become their guardians and Texas guardianship law requires that you follow very specific procedures. Plus, there is a child support issue here. You need to consult with an attorney in your area who handles guardianships; this website is an excellent resource for finding just such a lawyer. If you go to the "Find a Lawyer" section, you can search for a guardianship attorney by location. Best of luck.
Guardianships can certainly be complex, but they are inevitable in so many cases. To answer your question, the process begins with retaining a guardianship lawyer near you. An application would need to be filed for each of your nieces, requesting that you become the guardian of their person and/or estate. As it is unlikely that the children have any property of their own, you might be able to avoid guardianship of the estate.
Notice of the proceedings would absolutely need to be given to their fathers. Deadbeat as they might be, these men are entitled to the same due process as any other biological parent. When considering your qualifications as guardian, the Court would also consider the best interests of the children and the unavailability of the fathers.
I see that you're posting from the Plano area. I see issues like yours regularly in my
Dallas / Fort Worth practice, and I'd be happy to elaborate on the process if you'd like. You may reach me through the link below or through my profile on this site.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should never rely on this answer alone and nothing in these communications creates an attorney-client relationship.