I'm not sure what you're asking, because each parent becomes the origin point for what is considered local to it's children.
You might be using the wrong terminology. So I don't want to make assumptions and give you the wrong answer.
I've only tested in 2D with translations, so what I can say is that when you do a global transformation to translate a node, it is going to move it to that exact coordinate in world space, by offsetting it's local coordinates. In most cases with 2D, the world space is going to be the coordinates you see as the canvas that the camera will pan across. In 3D it's more like an abstract cube that holds all your objects. It's hard to say what it will look like, because it will be transformed into a desired camera perspective, then another transformation to cast it into a screen space.
Returning to the point, If a node exists inside a hierarchy, it will be locally transformed, relative to it's parent node, in order to achieve a position given by a global transform. If you want to preserve it's local space, so it may remain centered on it's 0,0 origin for example, then you will want to transform the root node instead. This is why I'm unclear by what you mean by ignoring it's parent relationship.
As an example that might help clarify this. Think of a node named B. It is a child of a node named A. If node A rests at 200x and 200y, and it's child node B is at 0x,0y, node B will also be at 200x, 200y in world space.
If you perform a local transformation that translates 50x, 50y to B, this will move it locally, adding the parents position and then it's own. So you will find node B at 250x, 250y in the world.
However, if you do the same transformation to translate globally to 50x, 50y. You're insisting that B move to the world space position of 50x, 50y. In order to do this, it must be translated locally by a negative amount. In this case it's -150x, -150y. It's local transformation will show it's translation now as -150x, -150y. Since it's parent rests at 200x, 200y, it must be offset locally to put it in that desired global coordinate.
I hope that was relevant. X)