I found this Blurb on google:
What are (final) dispositors in astrology?
"The sign any planet is in is affected by the sign of the planet that rules that sign. This is called dispositorship. So when Mars is in Cancer, it is heavily affected by the Moon, which rules Cancer. When Mars is in Leo, it will be heavily affected by the sign the Sun is in, since the Sun rules Leo. Mars in Virgo is more influenced by Mercury, and therefore whatever sign Mercury is in. Mars in Libra is affected by whatever sign Venus is in, since Venus rules Libra. When a planet rules the sign another planet is in, we say it “disposes,�?or is the dispositor of that planet."
There's a such thing as mutual reception, when planets are in the signs of each other (say, Venus--> Aries/Mars---> Libra), and final dispositorship is when you work through the chain of dispositors and you find a planet that disposits itself, with no mutual receptions anywhere, I think. This is supposed to give that planet a heavy amount of influence. Sometimes there's no final dispositor, and sometimes there is more than one.