I think noticed that my war fleets in a different sector sometimes capture ships. Is this completely random or are there certain conditions that have to be met?

Also, is there a way to tell the AI to capture a ship or do I always have to do it manually with harpoons?

[EDIT]

Yep, it's possible. All that has to be done is to equip one ship with harpoons and leave it in a sector with a disabled enemy fleet. Two conditions:
1. The enemy fleet has to be "at war" with the player.
2. Player's personal fleet (or at least the ship the player is flying) has to be in a different sector.
The harpoon ship will keep capturing the disabled ships in a random manner, one per day, but not every day - there seems to be a random chance whether it will attempt a capture or not each day. It has to be refilled each time a capture is made or each day (not sure which one; didn't do thorough enough tests).

I tested with Light Harpoons. I assume it's the same for Heavy.