How a modern railgun battleship might evolve

What would a modern battleship armed with railguns look like?

It would probably begin with 8-inch railguns and grow through an arms race toward 12-, 14-, and 16-inch weapons.

The first practical railgun capital ship would probably use an 8-inch weapon. That caliber could deliver great power while retaining a useful ammunition load and building on work associated with Zumwalt. Rival programs would then seek a larger advantage, probably skipping awkward 10-inch weapons for 12-inch systems. Further competition could move to 14- and 16-inch railguns. The answer treats caliber growth as an arms-race process rather than starting with the largest imaginable gun.