Any material you can recommend I can read more on that? As I understand it, the writings of Irenaeus get cited here to make that point except they're often taken out of context.
That's the only reason the Roman diocese became dominant. Not any sort of lineage or pedigree.
There's a very informative youtube video about the schism: https://www.youtube.com/watch?v=a6rWf0k8d78