To dominate the waves now a superpower needs to be able to
a) protect its own shipping, freedom of movement and trade
b) destroy any enemy fleet and trade and deny the enemy's movement, and
a) requires a significant force of escorts - ocean capable DDs and FFs and corvettes for shorter escort journeys. ASW is vital, from both the escorts and land-based aviation. Carriers make it easier, but I don't think they are essential for this any more, if you have long range strike aircraft (and now drones) with antishipping missiles and bases in the regions you want to control. However a fleet of minesweepers is required.
b) can be accomplished in different ways, but SSNs and land based aircraft are particularly good at this. Great big expensive cruisers and aircraft carriers are, again, not essential.