To precisely center a layer in Photoshop, use the following method involving selection and alignment tools.
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Select the layer you want to center in the Layers panel.
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Activate the Marquee Tool (M). This is crucial for the next step.
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Select the entire document: Press Ctrl+A (Windows) or Cmd+A (Mac) to create a selection that covers the entire canvas.
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Switch to the Move Tool (V). This tool allows you to move layers and also gives you access to the alignment options.
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Use the alignment buttons: With the Move Tool selected and the entire document selected, the alignment buttons in the top toolbar become active.
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Click the "Align Vertical Centers" button to center the layer vertically.
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Click the "Align Horizontal Centers" button to center the layer horizontally.
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Click both buttons to perfectly center the layer both vertically and horizontally.
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This method accurately centers your selected layer within the confines of your document. You can then deselect by pressing Ctrl+D (Windows) or Cmd+D (Mac).