Z_,
Yes, MOVE THE PLANES WITH THE CARRIER.
You may be confusing this with another action.
GAME EXAMPLE: During J1s COMBAT PHASE one(1) FTR from the carrier in the Solomon Islands sz(sea zone) flies to attack the the US AC, FTR and SS in the Hawaiian Islands sz(the Japanese AC stays put). If the Japanese FTR survives the battle(depending on what you threw into the battle) it can land on the Japanese AC. During the NONCOMBAT PHASE the Japanese AC CANNOT move to a sz that would be further away from the Hawiian Islands sz.
The Japanese AC could have joined the battle(during the COMBAT PHASE),
or moved one sz closer to the HAW sz(during the NONCOMBAT PHASE),
or move a maximum of two spaces(during the NONCOMBAT PHASE) to any sz within two spaces of the HAW sz.
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“Now, help the enemy meet Davey Jones!” - Xi