As referenced by Loial in The Dragon Reborn. Artur Hawkwing was a great Ta'veren. It seems that he stand out among other great hero in the Age of Legends. How does his Ta'veren property compare to the 3 Two Rivers boys?
"As the Wheel of Time weaves us into the Pattern, the life-thread of each of us pulls and tugs at the life-threads around us. Ta’veren are the same, only much, much more so. They tug at the entire Pattern—for a time, at least—forcing it to shape around them. The closer you are to them, the more you are affected personally. It’s said that if you were in the same room with Artur Hawkwing, you could feel the Pattern rearranging itself. I don’t know how true that is, but I’ve read that it was. But it doesn’t only work one way. Ta’veren themselves are woven to a tighter line than the rest of us, with fewer choices."