<<
However, I cannot find anywhere what determines "parentage" of a report
control.  That is, what is it that makes one control a parent and
another a child?
>>

I believe the parent is always the band the control is located in.  In the case 
of regions or subreports it's probably the region or subreport.

Therefore, if during processing, the band that the control is located in grows 
by (for instance) 1 inch the following will happen:

ShiftWithParent checked: this control will have its TOP property increased by 
the equivalent of one inch.
StretchWithParent checked: this control will have its HEIGHT property increased 
by the equivalent of one inch.

--
Larry


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