I have 3 fleets on a system, yet when the battle starts only 3 LCs and some escorts from those fleets show up, despite me also having 2 Cruisers on those fleets.

This is incredibly frustrating as I try to fight off superior fleets with my mediocre ships while I wait for one of them to die (and potentially lose an admiral because for some reason admiral ships always show up) so the rest of the fleet can show up.

You can order the admirals by moving the portraits before the Battle, this will set whose fleet turns up first up to your command point cap.

Warp out your ships that you don't want/are close to death then one of your ships from a replacement fleet will enter the match in your deployment zone.

@pinoklin Just switch your admirals to the biggest ships, then...in the fleet screen you can promote a ship to the new flagship.

Battles have a command limit, it is shown to you at the beginning of the battle, where you see the strength of both sides. There you are also able to decide which fleet should be sent in first, which second and which third. The command limit usually allows you to send in your whole first fleet and part of the second, at least the flagship of the second fleet plus maybe an escort or a light cruiser. If you warp out heavily damaged ships, reinforcements will show up on your edge of the map.