Assuming it turns out to be yours and you choose to be involved, which I would strongly recommend as this child could turn out to be best thing in your life.
Forget about a relationship with her for the moment and just provide support, do this via emails, inquire about the progress of the pregnancy, how she's feeling etc, attend appointments if you can.
At this stage she has no idea about the amount of work involved after the childs birth. Be there as much as you can for the child, to give her a break and so you get a chance to bond with the child.
If you're negotiating time with your child do so by email and always frame the email around "what’s best for the child".
Do your best to appear that you also have her best interests at heart whether you care or not.
Eg. "I'd like to have (bubs name) for the weekend, it's important for (bubs name) that he/she gets to bond with both parents. It's also important that you get some rest so you can be there for her/him.......blah blah blah"
Never ever get abusive in emails or texts, if she's pushing your buttons write what you'd like to say but don't send it, let yourself cool for a day, tone it down and reframe it as "what’s best for the child". Avoid personal attacks.
Get a diary and record ALL your time with your child, expenses, support etc.
Retain all emails, if you text a lot get a program that allows you to import text messages into word or excel. Make multiple copies of everything.
Keep your nose clean with the law at all times, never disclose to her anything that could be used against you no matter how well you are getting along at the time.
Do I sound paranoid yet? Consider these scenarios:
1. She meets someone else she considers better "Daddy material" and tries to shut you out to keep a tidy little family unit.
2. She decides to move 1000's of miles away.
3. You meet someone else, the child mentions how great your new partner is. She gets triggered/jealous and tries to limit contact.
4. She tries to reduce your time for more $$$.
Any of that, and more, is possible over the course of the next 15 or so years.
If you do try to rekindle the relationship give it your best but only once. As others have said sticking it out for the child will mean unhappiness for everyone.
My ex fell pregnant at the end of our relationship, "failed birth control" apparently. Truth is she saw this as her last option to have a child and knew I had the resources to provide support.
We tried to get back together for the child but this was a total waste of time. We worked well together for the first few years but she was always trying to draw me back in. When I started a new LTR she flipped and began limiting my contact with my son.
We’ve been exchanging solicitors letters and attending mediation for the last year and a half. Last week I had a major win in the courts. The judge blasted her for 20mins. She was making me out to be a terrible father but I could prove through emails/texts etc. that I had always been there for him and that she was an emotionally unstable controlling *****.
Wish I could have seen her face when the judge told her she needed therapy! I’ve ordered the court transcript so I can relive the moments the judge smacked her back into her box. It was absolutely beautiful; I’ll probably do a post here later and share my favourite quotes! It’s cost me more than $10K but was so worth it.
One last thing, if it’s a boy order the book “Raising Boys” by Steve Biddulph. I recommend it to anyone with a son. Sound advice on how to raise a man. The information in it runs parallel to a lot of the good advice you can find on this site.
Good luck, keep us posted.