No, they cannot be all brought through a Wraithgate together as they cannot meet this condition:

Commanders can order up to three formations of troops to follow
them when they make an assault, as long as all the formations
have at least one unit within 5cm of a unit from the commander’s
formation.

There is no measuring "off board".

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1. I would say the RAW allows this, although such a maneuver might warrant a die pinging off a forehead if it happened in a tournament.

EDIT: "There is no measuring "off board"." Hmm, I hadn't thought of that.  Nevermind!

2. I would say the units inside don't count toward the barging anymore than units trapped in a barging maneuver would count toward the assault.

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No,this was cleared up a few years ago by Jervis and I thought it was in the FAQ.
Units off board cannot use their abilities,so commander cannot be used to drag other formations through the gate.

It's no more possible than having a Marine Commander in a Thunderhawk draw along two other fully-laden Thunderhawks...

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No,the 2 units inside don't count as this would prevent any unit from assaulting the rhino at all.As you stated the opponent wouldn't be allowed to get 6 units in BtB with th rhino,also normal (non WE) unit that attempted to assault the rhino wouldn't be allowed as they would have gone BtB with 3 units.

I'd say the units in transports don't count towards the barging maximum because they're in the transport. In fact, I believe they are trapped within their transport as the Rhino counts as being in count with 3 enemy units.

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Poor wording on my part.  I meant 'participating', which they couldn't.

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author of Syncing Forward and other stories...

It's a dog-eat-dog world, and I've got my Milkbone underwear on.

I think we can safely say "no" to this one.

2. Barge and transports. If there is transports with units inside, do the units inside count for Barging? So if 3DC enemy (Warhound) engages into transports carrying units (like 3 Rhinos with Tacticals) do the Tactical units prevent more than 2 Rhinos being barged?

Heh, good one. While there is clearly one unit on the board (the rhino) the units inside do count for certain things like whether the formation is broken, etc.

I think the most sensible thing is to assume that the rhino simply counts as one unit.

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Here are the relevant sections highlighted
3.3.1 Charge Moves
When a war engine charges it is allowed to ‘barge’ any non-war engine units belonging to the target formation out of the way and carry on with its charge move. Move the war engine as far as desired, and then place any units that were barged out of the way as close as you can to their starting point, while still touching the base of the war engine that so rudely pushed them aside. The maximum number of units a war engine can barge aside in this manner is two per point of its starting damage capacity. Note that war engines may not barge other war engines out of the way.

The rule that no more than two units may move into base contact with an enemy unit when they charge does not apply to war engines. Instead a war engine may be charged by up to two enemy units per point of its’ starting damage capacity (ie, a Baneblade with a DC of 3 could be contacted by up to six enemy units).

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Sir Hemry Newbolt

1.  A more direct point than "no measuring when off board" is that special abilities of units that are off board are not usable.  Commander is a special ability, so it doesn't operate.  The lone exception is the SC re-roll when applied directly to the SC's formation.

2.  No, the units inside don't count for barging or pinning.  All sections of the rules that deal with transports in base contact (1.7, 1.12 and 3.3) are written in terms that exclude mounted troops from being considered in base contact with the enemy.  Mounted troops counting as part of the formation as described in 1.7.5 doesn't contradict that.

Mounted units do clearly count as being in the formation for the total unit count.

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Neal