The tradition of Christianity in Ireland, Scotland, the Isle of Mann, Wales, Cornwall, and Brittany from the coming of St. Patrick in the 5th century through the Synod of Whitby, and into the Celtic Church's twilight and incorporation into mainstream Catholicism in the 12th century.
The tradition of the Anglo-Saxon church, separate from that of the ancient Romano-Briton church, which was established by the mission of St. Augustine of Canterbury in the 6th century, and would continue to thrive until the coming of the Normans in the 11th century.
One of the oldest, and now defunct traditions in the Western church was the Punic church centered out of Carthage, which was in its zenith under luminaries like St. Augustine of Hippo Regius, Tertullian, and St. Cyprian. It would stands from the 1st century until its gradual disappearance in the 12th century.
The tradition of Frankish Christianity which would have its official start with the baptism of Clovis in 509 AD, and have special variants based upon his Gallo-Roman foundations. It would, in time, become the unique tradition of the French Catholic Church which is still active in our world.
The Visigothic church represents one of the earliest stages of the Spanish church and should be distinguished by its later Mozarabic tradition. Writers of this period in Spanish history were still drawn to influences from Rome, Constantinople, and most notably, Carthage.
The nomenclature here is perhaps a little unclear, as the term 'Roman' is multi-faceted and ambiguous in antiquity. Here is the traditions of the church as they specifically apply to the late Western Roman Empire, Ostrogothic, Lombardic, Byzantine and Carolingian Italy.
The Various Germanic peoples converted to Christian at different times, but the famously, the Saxon peoples did not converted until 776 AD. Consequently the traditions associated with the German church are of a later period, and are commonly tied to the apparatus of the Imperial German state.
The bishops of Rome have historically produced a large body of documents relating to church government, its regional synodical authority, and its relationship to other major apostolic sees. Later documents are also immersed in the politics of the French and German states, as well as the tenuous state of affairs with Constantinople.