The title Emperor was exclusive to the Holy Roman Emperor and the Eastern Roman Emperor. Did that mean that all other, Catholic European monarchs were supposed to be under the HRE in some sort of hierarchy?
Someone here once claimed that the HRE > France > England in a chain of Western European states, but I can't find that post, nor can I find any sources indicating this.
Are there any explicit declarations of one European kingdom being subordinate to another?
In very, very broad terms, the Holy Roman Empire was one power among many, whatever its pretensions to being the inheritors of Rome.
The HRE never was a unified nation in the way that, say post-revolution France was. It was often a bizarre tangle of duchies, free cities, sub-kingdoms, contested territories, nooks, crannies and inherited lands that weren't really connected to the Empire at all. Each of those constituent parts loved fighting with its neighbors in the Empire and the HRE as a whole was at times hopelessly antiquated relative to other European powers.
To add to the complication, the Hapburgs had a way of taking the thrones of other European kingdoms. Charles V, for example, was simultaneously Holy Roman Emperor and King of Spain. Here's a list of all his titles, more or less, which certainly would make you think that the HRE ruled the world, but note that Charles was Emperor of the HRE and King of Spain. He held both titles simultaneously. The HRE did not take possession of Spain. They remained two different entities. Charles just happened to inherit them both because the Hapsburgs married themselves into many royal families around Europe. All the titles Charles held were like that. He and his family might own them for now, but that did not mean they were, strictly speaking, part of the HRE.
