Objects in hierarchies behave differently when they are transformed, depending on whether the objects are node-selected or branch-selected. You can also use the Child Transform Compensation command (ChldCmp button on the Constrain panel) to tailor the behavior to your needs.
For information on these topics, see Transformations and Hierarchies [Working in 3D Space].
When you animate a child object, its animation is always done relative to its parent (local animation).
When you animate anything in global, it's always done in relation to the world origin: it does not matter if your objects are in a hierarchy or not. Nothing is inherited if you have global transformation keys because they override any parent-to-child inheritance.
By default, children follow the parent when branch-selected, but you can change all that by using the Active option on the Options page of the Local Transform property editor — see Parent Constraint [Working in 3D Space] for more information.
If you select the Active option, you can also toggle the Constrain 
Position, Orientation, and Scaling options to determine each one's transformation inheritance individually. For example, it's common to constrain an object's
position and orientation to its parent, but not the scaling, so you could deselect the Scaling option to prevent the scaling from being inherited.
If you deselect the Active option, the global transformation parameters (instead of local) are marked automatically when you activate a transformation manipulation mode because the object does not inherit the parent's transformations. This makes it easy to key an object's global parameters immediately.
For example, you cannot key the global position or orientation of bones, but if you wish to animate a bone globally, you can prevent the bone from inheriting its parent's position or rotation by deselecting the appropriate Constrain options (Position or Orientation).
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