What I mean is, has a hegemon ever peacefully allowed another state to split global influence, or let them become dominant outright? Is there any reason to believe that future power transitions will be more peaceful?
As a related question, do you consider the United States to be a hegemon?
In current international history (by that I mean after 1648 when the Treaty of Westphalia was signed) there have only been two hegemons: Great Britain and the United States. For Great Britain, this is most apparent with the Scramble of Africa. For Example, when there was a confrontation at the fort of Fashoda between Jean-Baptiste Marchand (france) and Lord Kitchener (GB). Following this incident, they divided the areas between Lake Victoria and the Congo River water source. There have also been conferences like the one that took place in Berlin in 1884 that sought to control the scramble.
According to international relations theory, a hegemon can do several things to a rising power. These decisions are based on how the hegemon views the rising powers risk propensity and the nature of revisionist aims. (revisionist in this sense means rising state). For example, if the revisionist ins risk-averse and its aims are limited, the hegemon can do one of three things: 1. Engagement (appeasement); 2. Binding (alliance); 3. Mixed strategy of the two.
For more info, read Randall Schweller's chapter called "Managing the Rise of Great Power: History and Theory" this goes more in depth in power transition models; peaceful and aggressive
The transition of the title of hegemon from one state to another has been peaceful. Great Britain did not wage a preemptive war against the United States or any other state on the basis that it was close to overturning them as the most powerful state in the world. United States did not have to go to war with GB to become a hegemon. They fought alongside one another in World War II but GB was devastated by the war which mean that the relative power of the US was heightened.
TO answer your last question. By definition of the word, hegemon, the United States is one. Since 1945, it has established a hierarchical relationship based on hub-and-spoke model and direct-relationships with states, and it has created rules and norms that states follow. Granted, this does not mean that the U.S. rules over the world but no state has been able to create a system of relationships to replace the U.S. model.