Dispositor Tree
This approach to viewing planetary influences in a priority scheme or structure of influences may be a carry-over from "days of old" when there were fewer known planets and astrological tools. Essentially you create a chain of influences until you (hopefully) arrive at a final depositor.
For example, Mars in Libra is ruled by Venus (ruler of Libra, where Mars is), Venus is in Sag ruled by Jupiter, Jupiter is in Aquarius ruled by Saturn, Saturn is in . . . You go down this chain until you find an end-point. You may find several chains or end-points. Apparently the author uses a tree metaphor to help you understand what the primary planets are.
Although I always encourage everyone to explore as many astrological techniques and methods as possible, do be careful about what you choose to learn and incorporate in your actual practices.
For example, what will knowing the one or two planets that are the end-points of these chains do for you? Let's say the final depositor is Neptune. Let's also say that the tightest and most angular aspect in your chart is Sun-square-Moon exact, and Mercury-conjunct-Jupiter exact and in trine to your Sun -- with Sun on the MC. Meanwhile Neptune is in the 8th house and has no close aspect other than one which is 12 degrees away from something. Would you then assume that Neptune is more important than the aspect patterns noted? Of course not.
You need to ask questions and put everything into a "what if" category to decide which item seems reasonable and which seems questionable. I can only tell you that all of my decades long studies have led me to throw out anything that isn't virtually 100% reliable in almost every case. After awhile you end up with less to work with, but it always works. Still, do study and learn as much as you can. Just be carefully about what you accept unless you test it and find it truly useful. Dave