We were beginning to drift off topic so I have moved our posts to a new section entitled "Data Quality"
I have no idea even what the formal definition of an entity model is
Well, I don't think that there is a "formal definition" of an entity model.
This is why I used the term "ad-hoc".
Unless you specify some quality rules then there isn't any distinction between an entity model, a real entity model and a bunch of ad-hoc entities.
They are just loose words that name an informal arrangement of diagrams.