Woody plants produce new leaves on old stems rather than just from below ground parts. Higher leaves have best access to sunlight, so woody species tend to dominate plant communities. The basic design of all plants is that the roots gather water and nutrients while the leaves gather sunlight and carbon dioxide. The leaves produce sugar and other reduced carbon compounds which must be transported to the roots to sustain growth and function. In woody plants the upward transport of water occurs on the inside of the stem and the downward transport occurs outside the upward water transport just under the bark in phloem. Girdling removes the bark and the phloem layer and thereby starving the roots (which continue to transport water to the leaves for some time).
Any size woody stem can be girdled, but it is most commonly done on stems 2-20 inches in diameter. Some girdled individuals are able to repair the damage of a girdle, a process referred to as jumping the girdle. For that reason some managers treat the girdled section of the stem with herbicide to prevent jumping.
The Woodworth prairie has no large woody stems, but we have girdled stems (grey dogwood and green ash) that are as small as a little finger. For dogwood the girdled stem dies, but so far we have not gotten rid of an entire patch with this method.
I prefer girdling to the much more widely used technique of cut, herbicide stump, pile cut top, burn brush pile. Here are the reasons girdling is a better way to remove unwanted woody vegetation.
If girdling is so much better biologically, why is cut-pile-burn the most widely used practice? These are my opinions. First, there is the aesthetic of making the work obvious (our pile shows how hard we worked) and neat (we did not leave a mess). Second, girdling result in a slow death and provides time for many individuals observe that someone is trying to kill a tree. It stresses many people to be reminded of death. Third, people like to work in groups and stay together. With cut-pile-burn the group does not cover much ground and they come back to that place for subsequent stages of the activity (rarely is the pile burnt on the day it is constructed.) Fourth, after death the woody stem remains standing for some time. If the girdled stem is a tree, one has the potential for damage to someone or something when it eventually does fall and associated legal liability. If the girdled stems are small trees, there is an aesthetic problem of dead twigs that persists for a few years.
In conclusion, cut-pile-burn offends fewer people and it pleases workers, so it continues to be the preferred technique even though it is not efficient (measured in restored area per person hour effort).