@Dejmar,If I understand it right, a stationary policeman will do no good. The Star Lord can circumnavigate, grabbing 50%. Then, the Star Lord can turn 90 degrees and cut off an additional quarter, then turn 135 degrees and cut off an additional eighth, and so on.
Here's myguaranteed bad answer (because it, too, allows SL to get more than half).
As I understand it, P restricts SL not only by threat of capture, but by driving SL into SL's already-captured territory. This doesn't stop SL, but at least he isn't capturing additional territory. But, since they have the same speed, is it even possible to prevent him from moving to the other side of his already captured territory and adding to it?
This a tough puzzle.