Against Royal Navy the German battle ships definitely would have needed carrier protection and vice versa. One carrier alone sounds way too small a force for that! But together with Tirpitz and Bismarck and escort that sounds like Kursk on the Atlantic...
Anyway, some data in the net:
Messerschmitt's proposal for a shipboard fighter was designated Bf 109T (T for "Trager").
All work on the Graf Zeppelin was halted in May of 1940. Assembly of the 60 Bf 109T-1 fighters was also halted at the same time.
Fieseler Werke was instructed to complete the 60 Bf 109T-1s then under construction but to remove the naval equipment and deliver them as land-based fighter bombers suitable for operation from short strips.
Stripped of naval equipment and fitted with a rack for a 66 Imp gal drop tank, 4 110-lb bombs, or a single 551-lb bomb, the planes were redesignated Bf 109T-2. It was concluded that the Bf 109T-2 would be ideal for operation from small, exposed airstrips such as those from which the Jagdflieger were forced to operate in Norway. Several units operated with the Bf 109T-2 in Norway.
However, it never operated in its intended shipboard role. The short-field performance of the Bf 109T lead to surviving Norwegian-based Bf 109T-2s to be based on the tiny fortified island of Heligoland in 1943. The last of the Bf 109T-2s disappeared from the inventory at the end of 1944.
On May 13, 1942, orders were given that construction on the Graf Zeppelin be resumed, and that it should carry an air group of 28 bombers and 12 fighters.
By this time, the Bf 109T was considered obsolescent for shipboard operations, and proposals were solicited for new carrier-based fighters. The Messerschmitt company submitted the Me 155, which was basically a navalized Bf 109G. It had a fuselage basically similar to that of the standard Bf 109G, but with an entirely new wing. The undercarriage retracted inwards into wing wells, providing the wider track required for safe carrier landings. Standard naval equipment such as folding wings, catapult spools, and arrester hooks were fitted. The powerplant was a 1475 hp Daimler-Benz DB 605A-1 liquid-cooled engine. Armament was to be one engine-mounted 20-mm MG 151 cannon and two 20-mm MG 151 cannon and two 13-mm MG 131 machine guns in the wings. Estimated maximum speed was 403 mph.
The Me 155 project was to evolve into a design for a single-seat bomber, then into a high-altitude interceptor. In August 1943, the project was transferred to Blohm und Voss and was redesignated BV 155.
The site includes data on Ju-87 production as well:
http://www.csd.uwo.ca/~pettypi/elevo...er/grzepp.html
http://www.fact-index.com/b/bl/blohm...ss_bv_155.html