...I am using the java.awt.Graphics.drawString and drawImage methods to draw each part of my object. If I have set my graphics component's font to have a size of 12 say, does this mean that each character takes up 12 x 12 pixels?
No, it's a little more complicated than that, but still easily available. You'll need to call Graphics.getFontMetrics() to obtain the font metrics for the current font. FontMetrics provides methods for obtaining dimensions of a particular string for that font and graphics context, such as getHeight() and stringWidth(java.lang.String) . That should be all you need to center up any given string on your image.
Edit: You can find more detailed info on FontMetrics and handling text in the graphics context if you need it in the 2D graphics tutorial: http://java.sun.com/docs/books/tutorial/2d/text/measuringtext.html
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