As of right now, all of space is treated like international waters - vessels fly the flag of some nation and follow that nation's laws with respect to criminal

As of right now, all of space is treated like international waters - vessels fly the flag of some nation and follow that nation's laws with respect to criminal activity, and captains are given wide latitude to make decisions affecting the ship's operation which carry the weight of law. Disputes between vessels of different nationalities or involving foreign nationals on vessel are generally hashed out by the two nations governments. For violations of international law, any nation can claim jurisdiction. At first, everyone on mars is going to have family and assets on Earth, and thus earth based governments are going to have a lot of leverage. Of course oversight will be difficult, so if a company wants to do something illegal it could probably get away with it, but they'ed be more like mafiosos than royalty. I doubt we'd see any abuses on the same scale as say the east india company. After a few generations though there might be a sufficiently large population with sufficiently little connection to Earth that they may want to come up with their own law system. It's unlikely that any mars colony will provide much value to earth beyond national pride, so by that point they might face little resistance so long as they remain nominally under their parent nation's jurisdiction.