Soul Essence

"Champions, large minions, and large monsters drop soul essence on death."

I just want to clarify, does it only drop when YOU'RE the one that kills them, or does it drop when ANYONE kills them?

If it's the second one, then does your ally champions drop soul essence too when they die?

Also, when they drop, how long do they last for before they disappeared? And if your ally also have this rune, then does it mean they can pick it up before you, taking it from you?