Thank You in advance for answering our questions. Bare with the newbness, as about 12 of my friends (core MTG players) all use this account to settle MTG disputes.
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They do go on the stack, but once there, they exist independently of the source. So, in your example, you can Bolt the Assassin after it activates its ability, but the ability will still resolve even though the Assassin is dead.
On the other hand, if you Bolt it first, then they can respond by tapping it to destroy a target tapped creature.
As the title said do tap abilities go on the stack?
As long as they aren't mana abilities. For example, the "T: Add G to your mana pool." ability of Llanowar Elves or Forest does not use the stack.
605.3b An activated mana ability doesn’t go on the stack, so it can’t be targeted, countered, or
otherwise responded to. Rather, it resolves immediately after it is activated. (See rule 405.6c.)
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Why bother with mere rulings when so many answers can be found in the Rules?
So you use Bolt, before the assasin dies can the assassin use its tap ability? Really? Wouldn't it die at the instant?
In general, players can activate abilities (such as Royal Assassin's ability) in response to Lightning Bolt as they can to almost any other spell (C.R. 117.7). And those abilities will get to resolve before Lightning Bolt (C.R. 117.7). Like any other spell, Lightning Bolt has no effect unless and until it resolves (C.R. 609.1, 608.2c). See also this thread.
So you use Bolt, before the assasin dies can the assassin use its tap ability? Really? Wouldn't it die at the instant?
An Instant is not... instantaneous!
As with (almost) all other cards you play, it has to spend some time on the Stack ( 'the waiting room' ) in case someone would want to respond with, say, Cancel, for example... or respond by activating Royal Assassin's ability!
'Instant' does not refer to the 'speed' a spell would resolve; it defines WHEN you are allowed to play the spell:
-Sorceries, Enchantments, Creatures and most others can only be played during your own Main Phase, while the Stack is empty.
-Instants, abilities (and spells with Flash) can be played (almost) anytime, but that doesn't make them resolve any faster.
You might want to read the section about the 'STACK' in the Basic Rulebook, or rule 117 of the Comprehensive Rulebook, if you feel courageaous...
can you in response lightning bolt royal assassin preventing the tap ability?
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On the other hand, if you Bolt it first, then they can respond by tapping it to destroy a target tapped creature.
As long as they aren't mana abilities. For example, the "T: Add G to your mana pool." ability of Llanowar Elves or Forest does not use the stack.
As with (almost) all other cards you play, it has to spend some time on the Stack ( 'the waiting room' ) in case someone would want to respond with, say, Cancel, for example... or respond by activating Royal Assassin's ability!
'Instant' does not refer to the 'speed' a spell would resolve; it defines WHEN you are allowed to play the spell:
-Sorceries, Enchantments, Creatures and most others can only be played during your own Main Phase, while the Stack is empty.
-Instants, abilities (and spells with Flash) can be played (almost) anytime, but that doesn't make them resolve any faster.
You might want to read the section about the 'STACK' in the Basic Rulebook, or rule 117 of the Comprehensive Rulebook, if you feel courageaous...
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules