"A sole dispositor occurs in a horoscope when one - and only one - planet lies in its ruling sign; and all the other planets lie in signs which, by a series of removes in rulership (disposition), work back to that ruling planet."
http://www.dearbrutus.com/sole_dispositor.html
Does that rule apply to a planet that is the only one in its own house, not sign?
Antares
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No the concepts are entirely different. Houses have nothing to do with sole or final dispositors. The usual term is final dispositor and a true final dispositor would be a planet in its own sign that connects through sign rulership (the houses have nothing to do with this) to every other planet. I seriously doubt there is a single legitimate chart that is like this. Using the 7 traditional planets it would go like this: Saturn in Aries, rued by Mars in Virgo, ruled by Mercury in Libra ruled by Venus in Leo ruled by the Sun in Cancer ruled by the Moon in Pisces ruled by Jupiter in Sagittarius. Jupiter is the final dispositor and is considered very strong because he is connected to each planet. I think the above chain is impossible, but you get the idea.
In reality what happens is we usually hit a a mutual reception or another planet in its sign, and the planet in its sign doesn't connect with the others. So Saturn in Aries Mars in Virgo, Mercury in Scorpio. Which brings us back to Mars. Still some astrologers refer to a planet as the final dispositor in any link of three or more. If there is a planet that is a final dispositor, it is worth studying in that chart as it might be of significant influence on the others.