First, if someone is stalking you, call the police each and every single time until his put in jail. It's better to be safe than sorry. If no one is stalking you, and you're just curious, I would have to say it is a power or control issue. I've watched enough Law & Order to support my answer. :) However, an obsession is something one cannot live without, so I do not think the obsession would be over once he has achieved the primary goal, but the control would increase or become more intense and may even result in violence, in my opinion.