No. Since there are no air bases on either island, it is a six-space move to get from Midway to New Zealand. A bomber could do it, but not a fighter. Incidentally, air units can fly over enemy units, so you wouldn’t have to control everything between the two islands.
Carrier-based fighter movement
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If at the start of my turn I have a sea area containing one carrier and two fighters (and no island bases), the fighters are obviously landed on the carrier.
Now, say I move the carrier into an adjacent sea area during Combat Movement. Do the fighters have to use one of their four movement points to enter the sea area (i.e. move independently), or can they move in with the carrier and launch within the sea zone?
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Aircraft of the same nation as the carrier do not move as ‘cargo’ on the carrier. Allied aircraft are cargo. They move independently of the carrier.