In what forms did autonomy/autocephaly exist in the West if at all?

[Nephi]

I've gathered, from my reading in various unrelated contexts, that the churches in Western Europe interestingly ranged in their autonomy from Rome, with some churches appearing almost completely independent (except maybe for the elevation of their primates?). It just seems that, like the East, there were autonomous (if not fully autocephalous) churches pretty early on in the West (e.g. France, Britan, etc.) and for a good while, but that they eventually became less autonomous and more just archdioceses/dioceses under Rome.

Does anyone know more about this or where I could learn more? Or even perhaps why autocephaly didn't develop the same in the West while churches in the East were getting granted autocephaly by the 5th century?

 

[Amatorus]

Weren't the North African churches de facto autonomous before the Islamic invasion? (Were they all western rite?)

 

[Minnesotan]

Weren't the North African churches de facto autonomous before the Islamic invasion? (Were they all western rite?)

There were large Arian and Donatist contingents there, too, in addition to the orthodox ones. The Donatists were of course autonomous in the sense that they regarded all other churches as illegitimate.

Some people have theorized that this may have made it easier for the Muslims to conquer the area ("divide and conquer", and all that).