Actually Edea didn't receive her powers from Adel. Adel was still a sorceress when she was sealed away into space( remember she planned to pass her powers onto Ellone when she was still in power in Esthar but was stopped by Laguna and co. before she could). When she died she ended up passing her powers onto Rinoa after Squall and Co defeated her.
Ultimecia DID pass her powers on. She passed them on to Edea when she appeared dying at the orphange, Edea herself also stated that she twice received her powers, once as a child (I think she was 5) from an unknown Sorceress and again as a woman when a sorceress on the verge of dying appeared to her (the game's ending proved this to be Ultimecia).
Edea also says that in order to die in peace a sorceress must be free of her powers. During the game this happens twice, when Ultimecia passes hers onto Edea and Adel passes hers onto Rinoa. Edea is also badly injured when she unwittingly passes her powers also to Rinoa. This makes me think that the only way a sorceress can pass her powers on is to either be on the verge of dying or badly injured, its probably a case of the sorceress' weakened body being unable to sustain her powers any longer,
Finally the possessed host of Ultimecia does not need to be a sorceress or witch already. Ellone was never a witch/Sorceress and Ultimecia's goal was to possess her in order to achieve time compression. She may have chosen to possess sorceresses because they already had a large amount of natural magic at her disposal but its certainly never stated in the game she needs to possess only a sorceress it could be someone who perhaps has higher magical properites within their body. In Ellone's case, she has the very special, unique ability to send people's consciousness' into the past and as for Rinoa, it may just be a coincidence but I'm pretty sure her magic stat is the highest out of all 6 characters when junctions to enhance the stats aren't applied, this could also be why she received Edea's powers instead of Quistis or Selphie Or she could have just been the nearest person.
The device Ultimecia uses to possess someone is the machine which copies Ellone's power, the only difference I'm assuming is that with Ultimecia being a sorceress, she is able to exert her will and control much more easily than how Squall and co. could through Laguna and co. Laguna and co stated they sensed some sort of presence around them during the times that Ellone took Squall and co, back to the past, so Squall and the others had some form of control.
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