TPA was created by utilizing the 2 dimensional projection of the 3 dimensional plane. Seems like 5 dollar words doesn't it.
The part of the club closest to the ground should point at the base of the plane. When the club in parrallel to the ground it should be parrallel to the base of the plane. With a laser attached to the shaft anyone can see the putter head works in an arc as the laser points along the base of the plane.
So is it the shaft plane? Just because the laser is on the shaft and points along the base of the plane does not mean the shaft is riding along the plane angle of the putter's shaft. Look at it this way, the golf club can be swung down the hands only plane, turned shoulder plane, turning shoulder plane, elbow plane, or squared shoulder plane, and it will still point along the plane line. However, the arc of approach of each of the planes will differ.
THe area of rotation during the putting stroke is in the Thorasic vertebrate region. This would mean the arms, hands, and putter are "locked" in and the shoulders are the only moving parts. So the plane angle is steeper than that of the clubshaft. No big deal, it just means the arc of approach and the arc of seperation will be different.
People, I believe, can get better visuals of arcs rather than planes. Being they are the same the putting arc utilized the arc. The alignment lines of the face are all square to the arc, not the target line, which makes it angled hinging rather than vertical or horizontal.
The tough part is that putting deviations can be nil if we expect to be great putters. It all goes back to practice and the demons hide in the details. Be specific in your practice.