When you move a layer in space, you modify its Position property.

You can separate the components of a Position property into individual properties—X Position, Y Position, and (for 3D layers) Z Position—so that you can modify or animate each independently. (See Separate dimensions of Position to animate components individually.)

Jeff Almasol provides a script on his redefinery website that places a new null layer on the line between the anchor points of two selected layers; you use a slider control on the null layer to reposition the null layer along this line.

To move selected layers so that their anchor points are at the center in the current view, choose Layer > Transform > Center In View or press Ctrl+Home (Windows) or Command+Home (Mac OS).

To move a layer so that its anchor point is at the center of the composition, right-click (Windows) or Control-click (Mac OS) the Position property, choose Edit Value, choose % Of Composition in the Units menu, and enter 50 for each of the components of the Position property.

To avoid softening of an image that is not moving, make sure that a layer’s Position values are non-fractional values. This avoids resampling that is used when a layer with image quality set to Best is placed on subpixels.