Of course they might like you and be attached to you.
You might miss them too, right?
The thing to remember in these situations is that her kids are part of HER reality.
Sooner or later, she will meet someone who will be the new step dad.
How will this make you feel if you realize you are now competing with him even on that level?
I know it is tough to say but you own them and her nothing, ok?
Legally, you have zero rights.
When she breaks up, you are no longer part of any decision making process concerning them.
Let's fast forward to a year later...
You met someone!
This girl is great and she likes you too!
How will she feel when she knows that you are still invested in your ex's children?
What if she has children too?
What if she is the one invested in her ex's children and they see each other a lot because of that?
How would THAT make you feel?
See the dilemma and the conflicting interests?
It is normal to dissolve everything that is related with her when she breaks up, not just the direct relationship you had with her.
To your power!