Personally I think the role of aircraft carrier would be rolled (pardon the pun) into the role of battleship, cruiser and destroyer. Since manoeuvrability is taken out of the equation then you'd want something that is capable of doing everything needed for a long cruise. Putting down 'Marines' on a hostile planet, check, protecting cargo vessels, check, providing a gunboat for diplomacy, check, humanitarian crisis, check.
Furthermore, since communications will be sporadic, these vessels will become their own nations in a sea of isolation, the captain/admiral/commodore/Legate will make decisions that will affect the homeworld without being able to check with them first. Perhaps that will require a group of diplomats or representatives of the homeworld to be on board? Likewise you'll need scientists and medical staff. So it's going to be a big ship, but if you're not needing to do the Kessel run then why worry about the size? Heck, you could go really crazy and just use a planet or a Dyson sphere.
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