and inflicts damage to the opponent's Life Points equal to half of the original ATK of the Tributed
Rulings for EctoplasmerYu-gi-oh! Card
"Ectoplasmer" causes the turn player to Tribute during his/her End Phase, but the opponent does not Tribute. So while "Ectoplasmer" is out, I Tribute in my End Phase, and you Tribute in your End Phase. But I don't Tribute in yours and you don't Tribute in mine.
So 1 Tribute is performed during the End Phase of each player's turn. The Tribute is performed by the turn player. (Both players have to do this during their respective End Phases, not just the controller of "Ectoplasmer".)
Tributing a monster for "Ectoplasmer" is not a cost, it's an effect, so you can't Tribute monsters unaffected by Spell Cards.
If you have a face-up monster on your side of the field during the End Phase, you have to Tribute for "Ectoplasmer"'s effect.
You can chain "Mystical Space Typhoon" or "Raigeki Break" to "Ectoplasmer"'s effect, and if there is no "Ectoplasmer" on the field, then its effect is not applied.
You can activate "Soul Exchange" during your Main Phase and use its effect to Tribute your opponent's monster for "Ectoplasmer" during the End Phase.
If you Tribute your opponent's monster that you controlled with "Snatch Steal" or "Change of Heart", your opponent takes the damage even though it was their monster.