I'm starting to run into that situation. I've been on the other side; after I left my first husband, I dated a couple of guys seriously before I met Hubby, and they met Alt and Country. And then when Hubby entered the picture, he very quickly became a parental-type figure to them.
I've seen the adjustments Hubby's had to make. He had no kids of his own; to top that off, before he met me his longest relationship had only lasted 4 months, and he'd never lived with someone in a relationship sense before. So that, combined with learning to be an adult authority figure to Alt and Country without appearing to take their father's place, combined with Alt and Country's needs (Alt has depression and anxiety disorder; Country is on the autism spectrum), put Hubby on an insanely steep learning curve. Sometimes he still struggles with understanding his role in their lives.
One of the guys I dated before Hubby had a daughter, but she was 19 at the time, so it wasn't the same dynamic at all. S2 is the first guy I've ever dated who has kids who are, well, kid-aged. I'm not around Spikes and Beads often enough yet for there to be any real issues, but it looks like I'll be seeing more of them.
So far, I've acted essentially the same with Spikes and Beads as I did when I was a teacher. As a teacher, I was in some ways a surrogate parental figure to my students when they were with me. As an aunt to my ex-husband's nieces and nephews, same thing. The ultimate discipline wasn't up to me, particularly in the latter case; I was more of a supervisor and someone the kids enjoyed talking to and hanging out with, and that's pretty much where I'm putting myself with Spikes and Beads for now.
With Beads, there isn't as much interaction because of the level of his autism. He doesn't often speak to others, so when I'm around he usually only talks to his dad. He'll smile at me and if I say something to him, he usually acknowledges that I've spoken, but that's about it. With Spikes, on the other hand, he's a very intelligent kid but is used to adults "talking down" to him; I've never been the type to "talk down" to kids, because I was raised by parents who didn't do that to me. So I have conversations with Spikes that, according to S2, leave Spikes feeling respected and proud of himself. (Apparently after the first time the boys met me, Spikes actually told his dad, "I really like her, because she treated me like a person.")
In some ways, forming a bond like that goes further toward taking a role in a kid's life than disciplining them and setting rules; I found, particularly with the students I worked with who had some pretty major behavioral issues, that when they believed I respected them, they were more inclined to treat me respectfully and behave more appropriately.