As I'm not sure if those explanations were clear enough, I'll try to synthesise here:

• Deleted entity passed to persist. One entity, supposed to be deleted, is still referenced / accessed. In my case, I had a problem with "cascading". The behavior I expected was "on delete cascade" and "on update cascade". I have those constraints well in the database, but they weren't right in the Hibernate annotations. After I changed that, the error stopped. While I was searching why I was getting this error, I've seen people whose problem was different. They had, let's say, a list of entities. Those entities were related to others, and, when deleting, they had to take care of deleting both the link and the persisted entity. This was the most common scenario of this problem, and is better explained here, for example.
• Detached entity passed to persist. One entity, which is supposed to be up to date but is not, is passed to persist. In my case, I was trying to create an entity (an Operation), related to another (the Account where that Operation was taking place). The persist action was failing because my version of the Account was incorrect. The solution was just to update the entity.
• Id to load is required for loading. Trying to access an entity without giving an actual identifier. In my case this was the easiest problem: I was calling find passing a non initialized long. Passing the correct, initialized values fixed the problem.