Should payroll be HR or finance?
Operationally? I would classify Payroll as Human Resources (HR) over Finance for key several reasons.
However, when it comes to the reporting and authorization of payroll, those functions should not be delegated to HR. Segregation of duties is key for proper internal controls of any company.
What I have seen is that at large companies HR has the Payroll function. HR usually has an accountant on staff who handles the payroll as it involves a lot of calculating and reporting. At small companies, it can go either way. But Mr. Morales's point is a good one that segregation of duties is needed.