use a humboldt face cut that is over one-half of the diameter of a dead vertical piece and you will have undercut the center of gravity. Use relief cuts below what will be the hinge, to prevent the bark from tearing down into your climbing system, and backcut. They will tumble off without a pullrope, and your will have more directional control.
By using a humboldt instead of a conventional facecut, you will allow the wedge to slide out. It doesn't have to be a very large, wide angle facecut.
I have done this on large Doug-fir mostly, dropping wood that I had to double cut with a 20" bar, 10'+ sections. Works a lot easier than a snap cut. Saves hauling up a pull rope and occupying a groundie.
I wouldn't want to try to use a snapcut and a pull rope. When the piece breaks free, it is just perched, without any directional commitment.
As mentioned about, length of piece in relation to height above ground of cut will dictate part of whether it falls flat or on end.
I imagine that the angle of facecut, and type of facecut will play into this as well.