The structure that catches the product of a Graafian follicle as it leaves the ovary is the fimbriae.

Here's a breakdown:

* Graafian follicle: This is the mature follicle that contains the egg (oocyte).

* Ovulation: During ovulation, the Graafian follicle ruptures, releasing the egg into the peritoneal cavity.

* Fimbriae: These are finger-like projections that extend from the fallopian tube (also known as the uterine tube) and surround the ovary.

The fimbriae have a couple of important roles:

* Catching the egg: The beating cilia on the fimbriae create a current that helps guide the released egg toward the opening of the fallopian tube.

* Transporting the egg: The egg enters the fallopian tube and is transported towards the uterus.

Let me know if you have any other questions.