What part of the roman empire did the envaders spread?

Which Invaders? In the empire of the west tin the fourth century Germanic peoples invaded: Franks, Alemanni, Visigoths and Burgundian took Gaul. The Visigoths, Alans and Sueves took over Spain and Portugal. The vandals took over Africa. Angles, Saxons and Jutes and Frisians migrated to Britain in waves. The Lombards invaded Italy in the next century.

The empire of the east suffered a similar fate, though much later. The Arabs took over the Middle East south of Turkey The Bulgars, Serbs and Croats took over the Balkans. Then the Seljuk Turks took over much of Turkey. Finally the Ottoman Turks conquered Constantinople.