This is a rough attempt to illustrate the role of CVs in GB2. I run a UK Malta CV (CV5)
or UK Illustrius (PCV). My BO is L116. I am not a noob. Here is how I see the role of
CV. I am open to suggestions if my "opinion" is wrong. Being a Flagship has only a
couple of differences from non-flag CVs. Assuming the game splits with 20/8, these
are your primary and secondary responsibilities and objectives:

1) Protect BBs. This means keeping fighters up and available to intercept bombers
(DB/TBs). Keep an eye out for messages from team mates about "incoming
bombers" or other problems.
2) Destroy Scouts. This means shooting down enemy scouts that provide
sight/vision for enemy to see your team.
3) Destroy enemy Fighters. This is the hard part. High level fighters will eat your
fighters up, but you have to send your guys up anyway. Even T1s can take out T4s,
if you have enough of them. Don't "save" your fighters during the game, get them
up and in action during the entire game. If you burn through all your fighters, just
accept that as the cost of doing war.
4) Scouting duties. It is NOT the responsibility of CVs to provide scouting duty.
However, if you don't your team may lose. Wasting fighters on scouting duty is the
cost of the battle to win. Most scouts sent up get eaten up by enemy fighters or
blasted by AA. If enemy fighter coverage is strong, your BBs can't send their own
scouts up through the thicket of fighters and vision/sight is unavailable. That also
means sending fighters on missions to provide sight/vision with no return for fuel.
You have to do that. Of course, if you are low on fighters, they need to return for
your own protection, but most CVs pack enough fighters that you can afford to lose
most of them.
5) Bombing duties. Always keep a TB or DB available. Let the BBs handle the
destruction of the enemy forces. Use your TB and DBs selectively and as necessary
to ensure victory, don't waste bombers on easy targets that the BBs will get
anyway, use them for long-range targets (enemy CVs) that are out of range of BBs'
guns. Again, don't expect them to return to ship, they are expendable.
6) Flagship duties. Don't get sunk. That means maintaining Fighter protection from
enemy bombers, bomber protection from enemy subs/ships, and always bring an
escort with a sonarman and AA setups. You should pack Hedgehogs to protect you
against subs (your most dangerous enemy). Don't take too many risks and don't sit
in one spot, move north, south, and change position constantly.

What to do when starting the game:
1) Launch your fighters and assert dominance in air superiority. (see items 1-3
above). Only after air superiority is achieved should you consider bombing
strategies. If you can't get air superiority, then your bombers will never reach their
target anyway.
2) Stay away from the firing (BB) line. You need to be a good distance back from the
battleships, as they need to maneuver and don't want you in their way. Keep your
escort away from them too. If an enemy BB moves in quickly, you could fall inside
their gun range and be toast. YOU WILL BE THE PRIMARY TARGET, IF AVAILABLE, TO
THE ENEMY. Also, enemy SS will abandon hunting BBs and go straight for you.
3) Be near the firing (BB) line. This means work with the BBs, but not too close, help
them with your fighter coverage and defense. If you are too far back, then it takes
a while for your fighters to get over your own BBs, you can lose a friendly BB due to
your tardy arrival. Take advantage of your team's AA and ASW supports in providing
cover.
4) Help your team achieve victory. This means adapting to the changing dynamics of
the game. Work towards identifying and supporting destruction of the strongest
(BB6) ships the enemy has. Keep your enemy blind from your team's ships and keep
the enemy under surveillance constantly. TBs are one of the only a few weapons
that work against submerged submarines. Learn how to manually control them and
your team will appreciate their work. Also, use your bombers to eliminate support
ships (ASW/AA). If your team's subs are in danger from ASW, try and help them by
taking out the DD/CL.

NOTE TO BBs:
It would be really nice if BBs helped anyone other than themselves.

If BBs would hit the AA or ASW ships (if available), the strength and power of Subs
and CVs would increase substantially, increasing sight, vision and control. Too
often BBs are more concerned with sinking another BB than hitting a support ship,
however, if that support ship was sunk, then our CVs could achieve air superiority
quicker. I have had to waste many bombers just to take out an AA ship, when the
BBs could have sunk him earlier. It's a lot easier to bomb a BB than a Moltke. Any
help from the BB class is really appreciated.

Remember this important point: GB2 is a battleship game, with everyone else in
support. However, it also requires support ships. Without ASW, subs would eat BBs
up. Without AA ships, DBs would eat BBs up. If you don't act as a team, then you
will lose. Guaranteed. The best teams work together. Losing teams work by
themselves.

Open for comments and suggestions.