Hi,
It deepends on the size and the structure of the organization. In a small organization wherein only the Manager HR is hading the entire function of the department is responsible for smooth functioning of the same.It may include all the funtions like recruitment, PMS,ER,T&D etc..
For the large organization where HR is divided into many sub department like PMS,Training,Generelist,Payroll etc, the owner of the sub departments are responsible for the smooth functioning of their respective area.
I would able to give you in detail if you can be give me idea for what kind of organization you are looking for this information.