When Eye of Singularity enters the battlefield, destroy each permanent with the same name as another permanent, except for basic lands. They can't be regenerated.
Whenever a permanent other than a basic land enters the battlefield, destroy all other permanents with that name. They can't be regenerated.
10/4/2004 If a copy card enters the battlefield, the permanent it is copying is destroyed and the copy card stays on the battlefield.
10/4/2004 Since phasing in does not cause enters-the-battlefield ability to trigger, it is possible to phase in a card which is already on the battlefield and not trigger this effect.
10/1/2008 This has the supertype world. When a world permanent enters the battlefield, any world permanents that were already on the battlefield are put into their owners’ graveyards. This is a state-based action called the “world rule.” The new world permanent stays on the battlefield. If two world permanents enter the battlefield at the same time, they’re both put into their owners’ graveyards.