Final answer:
The colonial assemblies had the most power among the royal governor, council, and assemblies in the colonial system. They had the power to initiate legislation, control the budget, and petition the monarchy for grievances.
Step-by-step explanation:
The royal governor, the council, and the assemblies all held different types of power in the colonial system. However, in terms of the most power, the colonial assemblies had significant influence. They had the power to initiate legislation, controlled the budget, and could petition the monarchy for the redress of grievances. They also had the support of most colonists because they were directly elected and represented the local entities that elected them.