What factors do influence the Project Management Level of Effort (LoE) on any Software Development Project?

1. The Organization. Many organizations have a "standard" or at least an expectation related to how much effort / overhead is usual.
2. The Deliverables. PM deliverables are living documents. There is creation effort in developing the project plan, risk management plan, etc. There is also ongoing effort in managing to / and keeping them up to date. This kind of effort can be estimated.

Project risk has bearing on the effort--higher risk (off-shore development, multiple stakeholders, new technology, non-dedicated resources) translate into more communication / coordination /issue & risk management effort for the PM.

Methodody (waterfall / iterative) plays a role as well in effort-by-phase.

On an "average" project (whatever that is ;-) I think the answer is something under 10% for LOE activities and (including deliverables) something under 25% for planning phase then trailing off as the project progresses. This is assuming you are doing "pure" project management and not writing use cases or whatever.