What is the greek word for fatherhood?

There isn't one single perfect Greek word that translates directly to "fatherhood" in the sense of the state or concept of being a father. The closest you'll get depends on the nuance you want to convey:

* Πατρότης (patrótes): This is probably the closest single word. It literally means "fatherhood" or "paternity," referring to the state or quality of being a father.

However, you might also use phrases depending on the context:

* Η πατρική σχέση (i patrikí schésí): This means "the paternal relationship," which is a more descriptive way to talk about the concept of fatherhood.

* Ο ρόλος του πατέρα (o rólos tou patéra): This translates to "the role of the father," focusing on the function and responsibilities of a father.

Therefore, while πατρότης (patrótes) is the most direct translation, the best word or phrase will depend on the specific context.