The adults I know who had intermittent contact with useless fathers have been more hurt and have lower self esteem then the adults with fathers who were completely absent
This!
I did similar to whatsernames friend and kept everything I had in writing, I tend to keep such things anyway but once I accepted my ex wasn't really interested in being dds father I planned for a potential future issue of him getting back in touch or her seeking him out and him blaming it all on me when actually I'd bent over backwards to facilitate the little contact he had in the early days.
Dd actually caught on due to something he did far earlier than I'd have liked and she confronted me about my covering for him (for her sake not his) and I had to admit I had not only been doing all the running but covering all expenses too.
At that point dd herself decided she wanted to know if he would make the effort or not and asked me to stop (by this point I couldn't afford it anyway) and I was sadly proven right.
Within 6 months he'd all but disappeared from dds life, by this point she was in high school and had her own phone, email address and sm accounts and so if he wanted a relationship with her without involving me it was perfectly possible, he just couldn't be arsed.
It hurts, it's absolutely heartbreaking but quite honestly I always advise on such threads that if it's looking like he isn't interested let him fade out of the kids lives as early as possible as this gives the kids a chance to forget them and not have years of being messed about, let down and repeatedly rejected. Which destroys them.
I hate my ex for what he's done to dd and there's nothing I can do about it.
You have the chance to handle things differently i recommend you do so.