Hi,
For procuring valuated stock items, cost center is not required and the GR will update the stock. If you are procuring non stock items with account assigned PO, or stock items with account assignment K, cost center is required. It means that you are booking the cost against the cost center and the material will be directly consumed against the cost center. No stock will be updated in this case.
Profit center is maintained in material master sales view or costing view. The same is required for different internal analysis.
You may refer the wiki: What is a Cost Centre - ERP Financials - SCN Wiki and the help doc:https://help.sap.com/saphelp_erp60_sp/helpdata/en/eb/13710f43c411d1896f0000e8322d00/content.htm
Regards,
AKPT