This a common misconception. Many Catholics *wrongly * perceive the Pope of Rome as the one superbishop with all the other bishops of world as his assistants or deputies. This is heresy and completely at odds with the Fathers. The Second Vatican Ecumenical Council settled this issue in light of misunderstandings of the teachings of the First Vatican Council. From the Catechism of the Catholic Church:
894 “The bishops, as vicars and legates of Christ, govern the particular Churches assigned to them by their counsels, exhortations, and example, but over and above that also by the authority and sacred power” which indeed they ought to exercise so as to edify, in the spirit of service which is that of their Master.
895 “The power which they exercise personally in the name of Christ, is proper, ordinary, and immediate, although its exercise is ultimately controlled by the supreme authority of the Church.” But the bishops should not be thought of as vicars of the Pope. His ordinary and immediate authority over the whole Church does not annul, but on the contrary confirms and defends that of the bishops. Their authority must be exercised in communion with the whole Church under the guidance of the Pope.
As a Canadian, I often use the analogy of the Canadian federation style of government. The federal government in Ottawa has jurisdiction over the entire country and the authority exercised by the Prime Minister / Ministry flows directly from the Crown via the Governor General (the Queen’s viceroy, or vicar if you will, for Canada). The premiers leading the 10 provincial governments likewise exercise authority received directly from the Crown via the Lieutenant Governors (the Queen’s viceroys in each individual province). The Provincial Governments may have a more limited scope of governance, but their authority still comes directly from the Crown and is not delegated at the whim of the federal government.