how much of the butt end of your club sticks out?

[Buffly]

I grip about 1/8" from the end... Basically, as close to the end without being at or beyond it. 

What is interesting to me is how many grip down might have a shorter wrist to floor or like a slightly more upright lie?

I play 2° upright so there is no need to grip down to go more steep for me. My wrist to floor is much longer than people my height by about 4 inches. 

The lie angle is dynamic where the relationship of static and motion measurements can be different. What is fascinating is how many OEMs build their clubs with different lie angles from club to club model which I can only guess is based on how far the COG is from the hosel pulling down the lie angle. (For instance, the Ping i500 and G400 irons do NOT have the same lie angles or gaps from club to club) Ping has a lot of ~3/4° increments then 1/2° in the short irons. 

Titleist has 1° increments in the long irons and 1/2° in the mid to short irons. 

Though most manufactures still progress in 1/2" length increments = all the more reason to be fit. 

Back to the original question of gripping down: this will lighten the swing weight or feel - which can be great if the shaft was too long or too heavy. The player can naturally get a feel for the best position for them without really knowing what is the reason. Other reasons could be incorrect grip size that choking down fixes it the grip was too big. 

All in all, as long as the player is consistent there is no right or wrong in where the player grips the club. 

I notice a lot of people address the ball with what I consider an awkward lie angle which can be with the club square to the ground or too upright. The tendency of the club head to droop slightly is natural so addressing the ball squarely to the ground would result in a flat impact which choking down might help fix. Secondly, addressing the ball with the club too upright created a flinch at impact to raise the handle or severely cover the ball. The ideal address has been explained to me as the hosel to the middle of the club face touching the ground and the middle to the toe be just off the ground. This slightly upright address position allows for square impact because of the slight droop during the dynamic swing. 

I have heard players, LPGA and PGA, try to explain how they grip down on the club as more habit from when they were juniors. Some have been quoted as having clubs built over length, but where they grip is actually close to standard length. 

I have also seen taller players almost have a 3 finger grip with the pinky hanging off the club which basically is like playing the club 1/4-1/2" over length. 

Finally, gripping down progressively farther down the shaft as the clubs get longer (about 1/10" to 1/8" per club) is basically getting closer to an MOI matched set, or same feel, rather than a swing weight matched set. I am no expert on MOI matching and I have spent a lot of time reading about it to the point of giving it a try.