That's an interesting question - I'd answer with 'both'. They're as you've noted branches, and they're young enough (and not woody) to detach and grow them as pups and into separate plants, I'd guess. I've never done it but I think it can be done.

Thanks for the advice! I might get bold to try to detach and plant a couple to see what happens.

You absolutely should - it won't bother Mama in the least.

I didn’t know PT palms did this. I found this, hopefully it helps.