It's complicated...
First of all, there's
Fines and there's
Bounties. And then there's Notoriety.
Fines are, well, fines. You can pay them off at any authority office of the issuing faction (which sometimes may be hard to find) or at an Interstallar Factor (IF), without any repercussions, as long as you have no Notoriety.
Bounties are slightly worse. They give anyone scanning you (player or NPC) within the issuing authority's jurisdiction the legal right to shoot you and cash in the bounty. They'll have to scan you first, though - there's your loophole. As long as you can avoid getting scanned, you're ok

. You can also pay them off at any office of the issuing authority - but in this case, the process is called "hand yourself in" and you will be transported to the nearest (can be up to a few thousand ly, though) detainment facility. The same thing will happen if you're killed and the bounty is cashed in by your killer. In this case, you'll need to pay off the bounty together with your rebuy. Bad luck if this happens when you're in a combat ship with a minimal FSD and the detainment facility is a couple of hundred lightyears (quite common) away... Good luck if you want to (slightly)
shorten the trip to Colonia 
.
Fines and Bounties are linked to your ship. Switch to a different ship, and you're clean again. Transporting the dirty ship or modules off this ship is a bad idea though - you need to pay a multiple of the Fine/Bounty to get the ship transported or the modules cleaned up again.
And then Notoriety. Fines and Bounties you get for breaking laws - like scratching another ship's paint, pulling someone from Supercruise or loitering too long in a trespass zone. Notoriety you get for killing clean ships - doesn't matter if NPC or Player. 1 kill, one point. Notoriety decays slowly while playing the game (1 point per 2 hours, as mentioned) and is linked to your CMDR. While you have Notoriety, you can't use Interstellar Factors for anything. As to whether Notoriety is cleared upon death/detainment, you'll need to ask notorious players; I try to avoid that as far as possible (until now...).