I just realized this question is rarely asked: How do the Greybeards find inheritors? They are surely mortal people, right? But do they ever come down from the High Hrothgar into cities and villages looking for inheritors? I know that Balgruuf and Ulfric were students of the Greybears, but they ended up becoming Jarls. And it's obvious that they never get to meet Paarthurnax. So it can't be Paarthurnax kidnapping children to the mountains (nope).

    I know the game left out tons of things due to limited device performance (BTW, have you noticed that the Dragons Reach is bigger inside than outside?). So as a lore lover, I do believe the game presents a condensed Skyrim that is ok to add details in. Maybe there should be apprentices living in the High Hrothgar that are just left out? 

    The Greybeards is said to be a highly honored order in Nord culture. There are pilgrims on the 7000 Stairs (only about 1000 in game). But according to them, the Greybeards barely have any communications with them. So how do they get to know any young people, not to mention ask them to be apprentices? And I guess most teaching falls on Arngeir because he is the only one who can talk without killing people (Does this mean he is the least powerful of the four or on the contrary, he is the only one proficient enough to contain his power?).

    And, it came to me that would be very cool to role-play as a Greybeard apprentice. I might change my profile image into one later. XD

The greybeards can sense su'um, even from very far away. They likely send some form of correspondence to individuals with promising strength. I seem to recall there is some information on their recruitment process on Ulfric's page on uesp.

KEAO

    And, it came to me that would be very cool to role-play as a Greybeard apprentice. I might change my profile image into one later. XD

I'm planning to eventually make a character based on Gongsun Sheng from The Water Margin. Guy's a battlemage known for controlling weather and shooting fire while also fighting with a sword, and in his downtime he studies Daoism. Replace Daoism with The Way of the Voice and he'd be a good fit in-universe.

Sonaak Kroinlah

The greybeards can sense su'um, even from very far away. They likely send some form of correspondence to individuals with promising strength. I seem to recall there is some information on their recruitment process on Ulfric's page on uesp.

Like Cerebro meets a Hogwarts letter?