Ships regenerate 5% health in deep space/outside of influence zones, or when orbiting neutral star systems. This is without any special trait or modules.

Ships do not regenerate at all when orbiting star systems belonging to allied major factions or when orbiting systems of friendly/brainwashed minor factions.

In other words, as soon as I get the option to repair/refit my ships at another faction's systems, they stop regenerating there, while they regenerate pretty much everywhere else.

It is my understanding/my recollection from playing previous patches that it should be the other way around.