SnowyAngel--the pieces obtained on Coruscant and Dromund Kaas are "bind to legacy." You can locate a mailbox, type in your Republic toon's name, and send the item from Dromund Kaas to them.
And to answer the OP, almost all of them took <5 minutes. Except Kaas, where I had a devil of a time because others kept finding it and were too far away for me to get there each time. I gave up after 10 minutes, went back the next day, got it in 2 scans.
Tips on getting the thing: Look at where everyone else is scanning and don't scan there, but scan near there. They are likely near a part, and if they find it, a giant beam will shoot out. So might as well cover more area by scanning a little way away