The two things that I don't liked about Morrowind's and Oblivion's justice systems, were 1. when you commit a crime and get a bounty EVERY guard in the entire world automatically recognizes who you are, and the fact that you have a bounty, and 2. If you resist arrest you are hunted down forever and never get the option to surrender.
When you commit a crime only the guards in the town you committed the crime in should recognize you. The more bounty you get the more your wanted, and then more and more guards recognize you because by now there are wanted posters of you everywhere. Also when you resist arrest you should have the option at all times to surrender and go to jail or pay the fines, just like you could in real life. You still would have to serve time for all the additional bounty you received while resisting. In addition you should able to lie low for a while in which case the guards eventually stop actively hunting you.
Alright now on to the main point of the topic. Bounty hunters. If you have a high enough bounty the government should send bounty hunters after you. If you have a low enough bounty they try to take you alive. If you have a very high bounty they kill you once they find you. They would range in skill from some guy with delusions of grandeur, to professorial bounty hunter teams. For each one you kill you get one infamy point and the chance to live another day. Family members of people you've killed should also be able to send private bounty hunters or assassins after you. In addition to being hunted by bounty hunters if you have a bounty, if don't have a bounty you can also join a bounty hunter guild and chase after dangerous criminals if you feel like playing a good character.
(heres a random fun fact. Do you know that the government actually still hires bounty hunters today to chase after people who've skipped town after paying bail?)