In the past month, I have had two rules arguments around similar scenarios. I have Prossh, Skyraider of Kher, numerous tokens, and Blood Artist on the battle field. I sacrifice all of them, but my opponent responds with Abrupt Decay (the first game this came up) or Pongify (the second game this came up in) targeting Blood Artist. They tell me the sacrifices are on the stack underneath their removal, but when the removal resolves, there will be no Blood Artist triggers.
From what I told them both times, is that the triggers go on the stack, and stay there, even if Blood Artist is removed. Am I correct in this assessment? And does this situation also apply to other death based triggers like Vicious Shadows, Falkenrath Noble, Rage Thrower, and Stalking Vengeance?
In general, while a player casts a spell or activates an ability, no other spells or abilities can be cast or activated or even resolve (including those that would keep the player from paying the spell or ability's costs, such as Abrupt Decay or Pongify to destroy the creature that would be sacrificed for Prossh's ability), because players don't have priority at this time (C.R. 601.2a-i and 602.2a-b have no priority window until the spell is cast or ability activated). The exception is that the player can activate and resolve mana abilities if the cost includes a mana payment (C.R. 601.2g).
Note that you can sacrifice several creatures using Prossh's ability before passing priority, because a player who had priority to activate an ability gets priority after doing so (C.R. 601.2i).
Any abilities that trigger from a creature dying due to the sacrifices, including those from Blood Artist, Vicious Shadows, etc., will trigger and go on the stack, and those triggered abilities will stay on the stack no matter what happens to Blood Artist, etc. (C.R. 112.7a). (Such abilities are part of a category of abilities called "leaves-the-battlefield abilities"; as a result, they can trigger even if their source dies at the same time [C.R. 603.6c, 603.10, 603.10a].)
Because you sacrifice one creature, and not several, each time you activate Prossh's ability, and triggered abilities (including those from Blood Artist, etc.) go on the stack before you get priority again (C.R. 116.5), the triggered abilities on the stack will be ordered such that the ability triggered by the most recently sacrificed creature is placed on top; this can matter, for instance, in the case of Stalking Vengeance's triggered ability.
As a result, it matters what order you sacrifice the creatures. If you sacrifice Blood Artist before sacrificing the other creatures, it won't trigger for those other creatures, since it isn't on the battlefield anymore (C.R. 113.6). (Note that you don't "sacrifice all of them", since Prossh can't be sacrificed itself with its ability.)
EDIT (Dec. 7): Some rules were moved in Commander 2016.
EDIT (Nov. 3, 2019): One rule was renumbered with Core Set 2020.
From what I told them both times, is that the triggers go on the stack, and stay there, even if Blood Artist is removed. Am I correct in this assessment? And does this situation also apply to other death based triggers like Vicious Shadows, Falkenrath Noble, Rage Thrower, and Stalking Vengeance?
Note that you can sacrifice several creatures using Prossh's ability before passing priority, because a player who had priority to activate an ability gets priority after doing so (C.R. 601.2i).
Any abilities that trigger from a creature dying due to the sacrifices, including those from Blood Artist, Vicious Shadows, etc., will trigger and go on the stack, and those triggered abilities will stay on the stack no matter what happens to Blood Artist, etc. (C.R. 112.7a). (Such abilities are part of a category of abilities called "leaves-the-battlefield abilities"; as a result, they can trigger even if their source dies at the same time [C.R. 603.6c, 603.10, 603.10a].)
Because you sacrifice one creature, and not several, each time you activate Prossh's ability, and triggered abilities (including those from Blood Artist, etc.) go on the stack before you get priority again (C.R. 116.5), the triggered abilities on the stack will be ordered such that the ability triggered by the most recently sacrificed creature is placed on top; this can matter, for instance, in the case of Stalking Vengeance's triggered ability.
As a result, it matters what order you sacrifice the creatures. If you sacrifice Blood Artist before sacrificing the other creatures, it won't trigger for those other creatures, since it isn't on the battlefield anymore (C.R. 113.6). (Note that you don't "sacrifice all of them", since Prossh can't be sacrificed itself with its ability.)
EDIT (Dec. 7): Some rules were moved in Commander 2016.
EDIT (Nov. 3, 2019): One rule was renumbered with Core Set 2020.