Final answer:
After Charlemagne's death, the control of the papacy was contested primarily between the French crown, the Roman Papacy, and the Councils of Clergy during the period of the Great Western Schism.
Step-by-step explanation:
After Charlemagne's death, several parties struggled for control of the papacy. However, as per the context provided in the question, during the period of the Avignon Papacy and the Great Western Schism, there were three main contenders:
- The French crown, which influenced the Avignon papacy and sought to maintain the papacy within its domain for political control.
- The Roman Papacy, which sought to re-establish and maintain its traditional seat of power in Rome after the papacy's move to Avignon.
- The Councils of Clergy, supported by various factions within the church, who, during the conciliar movement, attempted to establish a more democratized and collective religious leadership structure, challenging absolute papal supremacy.
While this question suggests exactly three parties, it's worth noting that the broader power struggles often included various European royal houses, aristocrats, and even external forces such as the Holy Roman Empire, though these are beyond the specifics provided in the documents quoted and the timeframe immediately after Charlemagne's rule.