What happened to aircraft if their aircraft carrier was damaged?

Speaking as a former military aviation-type person myself, I can assure you that the U.S. Navy (and uncle sam's airplane army, which was one of the unofficial names of the branch I first served in, the USAF) had and have, STACKS of regulations governing when and where to land if your home carrier is unavailable.

I cannot speak of direct or familial experience in WWII, as my father was a bomber pilot in the European Theatre, but I learned quite a few of said Naval regulations after being re-activated and transferred to the Navy after having left the Air Force under Reagan's military buildup in the early 1980's (I never made it back into the air, but I spent a ruddy lot of time in Navy classes preparing to do so!).

In general, regulations governing the question you asked (where do you land if your carrier has been sunk) come into play WHENEVER you cannot return to your carrier, for any reason. You will be interested to know that these regulations were being followed on the very morning of the Japanese attack on Pearl Harbour, when several pilots from the U.S.S. Enterprise had been launched from her earlier that morning, with orders to scout ahead and land at one of the Naval Airfields on Oahu if return to the carrier was impractical (as it almost surely would be, given the weather conditions). They endured the famous attack which followed soon after.

Sadly, I have no idea where to find you an internet link for this, since I learned it even before joining the Air Force, several decades before the internet came into widespread use. You can find several references in the "History of WWII" series edited by Sir Basil Liddel-Hart, and more readably in one of the first books written about the Pearl Harbour raid, "Day of Infamy," by Walter Lord. You'll find even more info specifically relating to your question in Lord's follow-up work, "Incredible Victory," detailing the Battle of Midway.

I can best describe what I mean by "stacks" of regulations in general by analogy with one particular regulation I remember very well: AFR 35-10. This Air Force Regulation (which is what the "AFR" stands for) dealt--circa 1976--with the requirements for shaves and haircuts for active duty members, and consisted of TWELVE PAGES of utterly ineffable twaddle, which I can distil down to the following single sentence without any loss of content or clarity: "Members shall be clean-shaven at all times including the back of the neck unless in possession of a shaving waiver (issued for infections of psuedo-foliculitis barbi), and hair shall be trimmed so as to be above the eyebrows in front, tops of the ears on the sides, and one inch above the collar line in the rear, with sideburns not extending below the center of the ear openings, and 'muttonchops' prohibited." Now I admit the preceding sentence is a little clumsy, but really, TWELVE pages to replace it??

In an exactly similar manner, the particular volume of Naval Regulations dealing with the scope of your original question ("Where do you go if your carrier's been sunk?") I remember best (circa 1983) was sub-titled "Extended Operations," (It was a subset of "Standing Orders: Carrier Operations."), and it was over an inch-and-a-half thick.

A bit less than half of it dealt with situations of the "When you cannot return to your carrier," type, say about 125-150 pages, and in summary, it could be distilled down to the following few statements: "When return to your carrier is impractical, select an alternate destination for your group with the following priorities: First, save yourself and your crew(s) (Pilots are more expensive to replace than aircraft, despite being created by unskilled labor!); second, save the aircraft if practical (planes cost money too); and third, attempt to land the aircraft near enough to the current action to allow the operation(s) to continue if possible." In other words: land if you can on a nearby friendly carrier or airfield close enough to re-arm, re-fuel, and get back in the fight. If this won't work, try for ANY carrier or airfield you can reach, and only as a last resort, ditch near a friendly vessel.

These rules are surprisingly common-sense for military bureaucrats... if you ignore the obvious irony that in case of war, the very first casualty is the rulebook itself. Please bear in mind that the above reflects my best memory of a military manual I read once, nearly forty years ago. For a better answer, we'll need an actual, honest-to-Pete carrier pilot, and I think I know where to find one, so stay tuned.