It's the Unknown Sector in between Montalaar and New Income. The name Avarice comes from X3:Reunion, where you could purchase the sector in an auction, because some teladi tycoon lost all his money, or something like that.
The sector was called Avarice by him, but you could choose a couple of names (some of which have been introduced as sectors in X3:TC now. See: Legends Home and Gaian star).
And on topic: In my main game I have my PHQ set up in the pirate sector "Veil of Delusion". I simply -love- the way it looks. Nice thin reddish fog, with a white/yellowish planet in the background when entering the sector. If you turn to face the jumpgate again you can spot a lovely blueish planet on the background, left of the gate. In my game though I am on good terms with the pirates, and the hostile ones coming from the present pirate base (which happens to be quite far from the gate, opposite of where I dropped the HQ (exactly at 0,0,0)) do not bother me at all.
Some might say this sector is useless because there are no good resources, or equipment close by, but if you got the PHQ the legit way, you have 3 sets of gates at your disposal, so you can set them any-frigging-where you want
) and I was wondering about just where I should put it. I was originally thinking of putting it in Avarice but as I have a M7M missile mega-plex there I didn't want my HQ in a sector which has a "don't look this way" zone. 
