So, I've been seeing a girl off and on over the past 8 months or so. Well, now she's pregnant. We both agreed on an abortion, now she changes her mind. The reason we were on and off was because I found out she was cheating on me. Now here's where it gets straight out of a Maury show... Who's the father? I'm fairly sure he would take it and they would get together. However, I do not want the responsibilities, nor do I have the capabilities of being the best father possible. There are many reasons for this, here's a few...

I'm in my early 20's with a variety mental health issues that I actively am seeking help. I'm interning doing what I can, when and where I can in order to get into my field of work, which means I will be on the road probably 10 months a year. However at the moment I am still under 15k a year income. I truly believe, even if the child is mine, that I will not be the best that a child deserves. Due to the mother and myself's past relationship, it would not prove to be a healthy environment and for these reasons I think it's best that I not be considered the father, nor have the responsibilities of such. A paternity test is in the works, but if I am the father I don't want my name on the birth certificate, nor do I want to be held accountable for child support later on in the road. Like I said, I'm young. Is there anything else when drawing a legal document (just at least something in writing before I can get a family lawyer involved, also posting in /r/legaladvice) that I should be explicitly stating ? Any experience, advice, or just talking would also be appreciated.

edit: I was thinking LPS, not TPR.