Different companies have different answers to this question and I’ve seen very few that fall in line with the Project Management Institute’s view point. In short, the Project Manager is responsible for organizing the team, communicating to stakeholders and getting the project done. A Project Manager should be able to initiate, plan and execute and close a project. They should be able to manage the scope, timeline, risks and the budget. In some organizations they are responsible for staffing the project, managing everyone on the project team and procuring hardware and software.
In some projects the procurement is handled by a procurement manager who may get all the hardware and software for the entire company. Staffing in a matrix environment is usually handled by department managers. But the project manager should be ready and able to handle any of these responsibilities.