Fnds Center Auth. (Cross-Fnds Cntr and Internal) 
Use of cross-funds center and internal funds center authorizations is only significant in budgeting. You can use them to achieve more targeted control over budget allocation. The system checks the following in budgeting:
Whether budget processing is permitted in a budget structure element (funds center/commitment item/fund combination) which has a different funds center as its superior budget structure (BS) element
Whether budget processing is permitted in a BS element which has the same funds center as its superior BS element

The following hierarchies are given and you want to use authorizations to control budget allocation at local level:
You authorize the manager of center C1 to maintain:
The manager of center C1 thus has full authority over budget allocation within his or her center. He or she can allocate budget to the top commitment item (A) in the subordinate centers C1.1 and C1.2, but has no influence on the distribution to A.1 and A.2.
You authorize the manager of center C1.1 to maintain:
The managers of C1.1 and C1.2 receive authorizations for their responsibility areas.
For more information on local budget allocation, read
Principle of Budget Allocation in Funds Management .