I'm just wondering, say I shared a planet to my alliance mate, and they decide to ditch randomly and join another legion without even giving a reason.

If i take the planet back does it disappear from their list? (Since technically they didn't scan it.)

After 24 hours all shares disappear. Even if they don't leave your legion. You do not keep shared planets in your planet listings.

If you posses the planet then it stays in your scans unless fluxed. I know I have taken several from shares when the guy trying to get it cant and then I have given it to them and I can still see it days later. Usually I purge it later, but it does stay past the previous 24 hour mention.

opps sorry i didn't explain it properly... what I mean to say was, I shared and they occupied it, now if i invade it does it stay in their list? Or will it act like a "share" and dissapear after a certain amount of time

If they 'own' the planet, it is added to their database permanently unless you flux it.