I had relatively good luck.
Coruscant: 20 minutes, made a group, got it strangely were I started.
Taris: 30 minutes. Our group was competing with another. The piece ended up under a wall.
Dromund kaas: I came here twice on my alts, first time I didn't know I needed the scanner. About 20 minutes, did some instance swapping though.
Hoth was the most fun (fun fact: the "ambris's fury" is the place you got HK in the beta); as soon as we got here, we found about 25 meters (sounds like everyone had this). We were competing with a Sith, and eventually his 2 friends. Eventually, the Sith marauder dug it up. We grabbed it, and then the 5 of us, I a guardian, my friend a commando, a Sith marauder, a Sith sorcerer, and a sniper, had some good old fashion open-world PvP. We won.