Maybe I'm just dumb but, after reading through the rules and FAQ, some things are still not clear to me.

Suppose I attack my opponent's battlefield. I have a unit with power 3 and my opponent has a unit with 2 hit points. When assigning damage, I assign two damage to my opponent's unit and one to my opponent's capital. If my opponent somehow cancels one damage to his unit and it survives does the damage I assigned to his capital still get applied or is it canceled because I didn't "get through" all of his units.

Along the same lines... consider the same example as above but his unit also has Toughness 1. Am I compelled to assign 3 damage to that unit or can I assign only 2 to it because that's the number of hit points it has?

Lastly, suppose my opponent now has two units with which to defend and one has 2 hit points and the other has 4 hit points. I am still assigning three damage. Do I have to assign two damage to the unit with two hit points or may I assign all three damage to the one with 4 hit points if I really want to damage that unit?

You got it all right. FAQ 1.5 says

"the attacking player must assign enough
damage to destroy each defending
unit before any damage can be
assigned to the defending player’s
capital."

In order to hit the capital, this assignment must include any cancellation effects in play, e.g. constant effects via keywords such as toughness and you must have damage left to assign after doing this with all defending units before you can assign to the capital. You are free to assign as you like among the units which are defending, e.g. to make sure you destroy a unit and you can also overassign damage in anticipation to other damage cancellation effects that you suspect your opponent might play.

So for case 1: exactly as you describe.

Case 2: you have to assign 3 before you can assign damage to the capital.

Case 3: you can assign the 3 damage as you see fit.

Thanks for responding, tako. You say that I got it all right but I had some "is it this or that" type questions so, just to be abundantly clear....

wapcaplets said:

If my opponent cancels 1 damage to his unit in this scenario the damage on the capital still gets applied.

Along the same lines... consider the same example as above but his unit also has Toughness 1. Am I compelled to assign 3 damage to that unit or can I assign only 2 to it because that's the number of hit points it has?

In this case I must assign all 3 damage to the unit because Toughness 1 was in play and I have to take into account that effect when assigning damage.

Lastly, suppose my opponent now has two units with which to defend and one has 2 hit points and the other has 4 hit points. I am still assigning three damage. Do I have to assign two damage to the unit with two hit points or may I assign all three damage to the one with 4 hit points if I really want to damage that unit?

I am allowed to assign all 3 damage to the unit with 4 hit points.

If I have any conclusions incorrect please advise.

Lastly... in the final scenario, is it valid/legal to assign one damage to the unit with 2 HP and two damage to the unit with 4 HP if that would, somehow, be to my advantage?

wapcaplets said:

Yep, you can assign 1+2 to two units if you like. DElves in particular with their -HP effects might not need to assign = HP to kill of units, if not this turn, then in the future, ditto for the DElf destroy damaged unit Tactic.

Exactly, just in case let me go through it again.

wapcaplets said:

Yes, assuming that the unit did not have the cancellation effect in play already when you assigned the damage, in which case you would have to assign 3 (as per you case below). In your example, your opponent would e.g. play a tacticafter damage assignment that cancels 1 damage to a unit. This would not affect the damage assigned to the capital, the damage would not be called back or re-assigned.

wapcaplets said:

Exactly

wapcaplets said:

Yes, you can assign damage to the units in any distribution you like.

Thanks, everyone, for your thoughtful and concise replies. I'm going to an all-weekend Blood Bowl tournament and want to teach some of the guys to play Invasion and I want to make sure I have everything clear in my head before I do!

Very good idea and I wish you much success on your tournament!