Aircraft Carriers are naval ships designed to operate aircraft at sea.
The availability of carriers depends on the country operating them. The United States operates more carriers than the rest of the world combined and has most of them deployed at sea in different parts of the world. In the event of a zombie outbreak, these ships would be ordered close to land to conduct bombing missions and serve as offshore safe havens for evacuating refugees. If already deployed and the traditional command and control structure is overwhelmed by hordes, their crews would be isolated from the outbreak and most likely keep the carrier away from coastlines. If in port, a carrier could be boarded and used as a living space isolated from the outside if ways for the undead to walk onboard were blocked or destroyed. Unless most of the crew is present in port, being able to operate the ships and move them would be difficult as they require manpower and a knowledge of their operating systems.
As with any ship and/or offshore landmass (island), an aircraft carrier's advantage is being in the ocean and away from infested land areas. American and French carriers are powered by nuclear reactors, enabling them to remain powered at sea for as long as two decades. The main challenge of living on a carrier is living at sea for long periods. Depending on how stocked the ship is of food, how much of the crew is on board, and the numbers of survivors it may have taken on, food supplies will run out faster than normal. This requires using the carrier as a staging point to move smaller vessels or helicopters to land to scavenge or hunt for food, and/or find a way to fish over the deck. Fresh water would be available from the ship's own desalinization plants. Nuclear powered carriers have fuel enough for years, but carriers from other nations are powered by conventional engines requiring fuel, limiting their at sea endurance. This also goes for the other ships of a carrier's battle group; if escorting ships run out of fuel, the carrier may have to take on their crew. Some countries that have carriers don't use them very much, so they are in a state of disrepair and are not reliable when used.
In the likely event that a carrier at sea has its regular crew onboard, the ship would be safe from refugees pirating vessels. Along with weapons from other ships in the battle group, its own aircraft and defense systems could destroy any threat. Carriers themselves are large, making it difficult to board or sink; short of a rogue military vessel, the carrier is safe from attack by the average seagoing survivor. Fixed-wing combat aircraft have little effectiveness against zombies when bombing, and they may even be dumped over the side to make room for survivors. Helicopters are their most useful aircraft, as their ability to not need the entire deck to take off makes them ideal for moving people and supplies to and from land on scavenging missions. A specific type of aircraft carrier is the Helicopter Carrier, a type of flattop used by Marine forces for amphibious assaults. Though none are nuclear powered, they contain more helicopters than planes.
Whether nuclear powered of conventionally powered, an aircraft carrier will most likely not be able to sustain itself at sea. Conventionally powered ships will run out of fuel, and nuclear powered ships will run out of food and not likely be able to salvage enough while entirely at sea no matter how small the crew gets. The best use of a carrier would be to anchor it several miles off a coastline for close access to land resources while maintaining standoff. Even if a carrier runs out of fuel, the ship will likely survive the outbreak; all zombies will decompose long before rust and corrosion from ocean water makes the massive ships fall apart.