Final answer:
The Ostrogoths and Visigoths established their kingdoms in Italy and Spain respectively, blending Germanic and Roman cultures and adapting Roman bureaucratic and legal institutions to govern the territories they conquered from the Roman Empire.
Step-by-step explanation:
When the Ostrogoths and Visigoths took over Roman territories in Italy and Spain, the Roman structure of government underwent significant changes. In Italy, after the deposition of the last emperor in 476 CE by the Ostrogothic warlord Odoacer, the Ostrogoths established a kingdom with a pledge of nominal loyalty to Constantinople. This maintained a semblance of the earlier Roman imperial connection, although the actual control had shifted.
The Ostrogoth ruler Theodoric later established a stable rule that incorporated Roman institutions and governance practices. However, in Spain, the Visigoths, who were Arian Christians initially separate from their Hispano-Roman subjects, created written law codes in likeness to Roman traditions but faced uneasy relationships until the conversion of King Recared to Catholicism.
Acculturation, including conversion to Christianity and adopting Roman bureaucratic systems and diplomacy, facilitated the blending of Germanic and Roman cultures leading to the emergence of new societies in the Middle Ages, which ultimately replaced the Roman political authority.