This is what I've pieced together from the Rules Ref, all in one place for easy review. Corrections appreciated!

A ship that can dock in another may start the game either docked or separate. This decision is made after placing obstacles but before placing ships. [This probably goes to First Player for timing instead of using Initiative since it’s a “before Step X”-style effect. -ed.]

A docked ship may deploy voluntarily in the System Phase. Use the docked ship’s Initiative for timing. It may deploy from either the front or rear tabs of its carrier, and it may use any maneuver on its dial except Stationary and Reverse maneuvers. Deploying is executing a maneuver.

• If the ship cannot be placed anywhere on the template without overlapping other ships, the deploy fails and the ship remains docked.
• If the deployed ship leaves the map, it flees as normal.
• If the deployment is successful, the ship may perform one action . (Note: As written, this is not a Perform Action Step and still happens if the deploying ship overlaps an asteroid or only partially executes the maneuver.)

A ship at Range 0 of its carrier may dock during the System Phase. Use the docking ship’s Initiative for timing. Remove the docked ship from the map and put it in the reserves.

A ship that docks or undocks in the System Phase does not activate in that round's Activation Phase.

A ship cannot both deploy and dock in the same System Phase.

If a carrier is destroyed while carrying any docked ships, those ships may emergency deploy before the carrier model is removed. This works like voluntary deploying, except:

• The deploying ship first suffers 1 Critical damage.
• The deploying ship doesn’t get an action.

Docked ships that don't deploy are destroyed with their carrier.

An emergency-deploying ship may or may not get a chance to attack that round, depending on whether its place in the Initiative order has been fully processed already.

A docked ship cannot emergency deploy if its carrier flees because fleeing is a distinct event from destruction in 2.0.

A ship is in reserves while docked. Ships in reserve maintain all tokens, and they lose round tokens and regain standard and Force charges as normal each End Phase.

If a ship is using Emergency Deploy and cannot be deployed because of blocking ships isn’t it destroyed?

One addendum. If the deploy maneuver is partially executed, you deploy and take your action. If it would be partially executed, but you cannot be placed without overlapping another ship (emphasis added), then the deploy fails. If you do the latter on an emergency deployment, the ship is immediately destroyed.

5 hours ago, MarrowHawk said:

One addendum. If the deploy maneuver is partially executed, you  deploy and take your action   . If it would  be partially executed  , but  you cannot be  placed without  overlapping another  ship (emphasis  added), then  the deploy fails. If you do the latter on an emergency deployment, the ship is immediately destroyed. 

So basically, you are permitted to bump on a deploy, but you still have to fit on the table... if you can't fit on the table, then you can't deploy.

Here's another intriguing question... does a docked ship (or really, any ship that's in reserves) still engage? Clearly, it doesn't attack ... but does it still engage at its proper step? And if so, would it have to interact with effects that look for "when you engage?" For example, would it be required to roll for Console Fire, or receive an ion token for Disabled Power Regulator? For reference, the RRG states, under the section for "Reserves"...

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While a ship is in reserve, it is not assigned a dial, it cannot perform actions, and it cannot attack.

A Rule specific to the Nashtah Pup deploying:

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Q: When the Nashtah Pup deploys, does it gain charges equal to the charge limit from the ship card with the Hound’s Tooth?
A: No, when the Nashtah Pup deploys via emergency deployment, it gains the number of active and inactive charges that the ship with the Hound’s Tooth had before it was destroyed.

10 hours ago, irishthump said:

If a ship is using Emergency Deploy and cannot be deployed because of blocking ships isn’t it destroyed?

A docked ship is eliminated if its carrier is eliminated, yes. I figured that was obvious but I'll add it.