Adoption process interrupted

What is the name of your state? TX
I lived with my ex-girlfriend for almost 10 years. At that time she had a daughter, she's now 13 years old. I tried to adopt her but I never got to finalized the process. Also, we tried to adopt a boy(her sister's son, he was physically abused)almost 3 years ago, he was 6 months old, but it ocurred the same, we never finalized the adoption. A year ago we separated, I fall in love with somebody else, and for some time I was unfaithful to my ex, until I left her home. A few weeks ago, I tried to have her sign a letter saying that I would give her some money every two weeks for child support for her two children. She refused to do that and now she told me she's going to a lawyer to ask for child support.
My question is:
Can she do that even when we didn't go thru the whole process? The children don't even have my last name. How can I know what happened to the adoption process? I live in Texas. I really appreciate your advice. Thank you.

It is unlikely, if you and she were never married, that an adoption process was ever completed. Texas law appears to require that a stepparent adoption must be a spouse. Additionally, if you never appeared in court, it is unlikely that the adoption could have been completed. So, if you were never allowed to adopt , it is unlikely you could be held liable for CS. If she wants CS, the bioparents should be the one's she goes after.

Summary of TX Adoption law:
http://www.adoptionsolutions.com/general/state laws/tx_law.htm