There are several types of emergent factions.
The Western Roman Empire Rebels and Eastern Roman Empire Rebels are shadow factions, which means they emerge when a province of the Western Roman Empire or Eastern Roman Empire rebel. Once they are on the map, generals from both sides can rebel and join the other. They will also reemerge.
The Ostrogoths are similar, and will emerge when a province (but not the last, I believe) of the Goths revolts. They will also reemerge if wiped out, and another province rebels.
The Slavs emerge along the northern extremes of the map in 410 AD.
The Romano-British emerge if the Western Roman Empire no longer controls Londinium (Britannia Superior) or Eburacum (Britannia Inferior). They have a stack of experience troops, but will not reemerge.
If you want to play as the Romano-British, you'll have to download a mod.
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