Playing against a Medium opponent, I always find that the pirates will saunter about one of their systems before getting bored and travelling back to the base where they stay, rather than despawn. It usually results in pretty much every game of mine having a pirate base with hundreds upon hundreds of pirates at the base in the end.

Here's a screenshot example where I had to build an entire fleet just to take them down.

I wouldnt deal with them until I was ready to.

By that, I mean I had taken and fully developed all planets on my side of the pirates, then done all the research. Use the pirates as a buffer so that you have time to do things without worry of being hit.

I'd then produce a fleet maxing out all resources, and when all was ready, I'd hit the pirates with everything. 16 capital ships, and 300+ cruisers and frigates, is going to make a mess of any sized pirate fleet.

Then you split the fleet into an attack fleet, and a blocking force, reinforce the ex-pirate base and use it so that nothing can come through to threaten "your space" while you go take the rest.

Yes. Instead of having to go through combat, you can purchase levels.

If you werne't talking about that, then yeah, you could get a crapload of pirates on your door and whipe them out. . . ALL OF THEM.

Yes. Probably evaluates all trade, though.

Edit does not appear to be working at all.

It's called "Plundered Booty" and it gives +3.5 to tax income (so pirate bases are virtually always positive, since they support no population). The actual income rate still fluctuates according to the base's alleigance.

Really, as long as any raiding ships are destroyed, the fleet at the pirate base will not grow, since the base only gains ships from those that survive raids and manage to get back to the nearest pirate base.

It may also be a good idea to take out a pirate base in a system you already control so you have one less thing to worry about in that system.