As a PM, based on what do you assign risk owners?

The risk owner should be capable of managing the risk and have the knowledge, resources, and authority to deal with the risk. Selecting the risk owner thus usually involves considering the source of risk and identifying the person who is best placed to understand and implement what needs to be done

I would do CPM/PERT. Critical path/milestone will be the deciding factor for me. Budget and timeline is another factor that cannot be overlooked.