I think I should have left the "End of process." in the quote, because this makes more sense. It's not the end of the process. The taxing authority sends you an estimate, you adjust based on a few factors they didn't account for and send it back.

That still raises the question, though, of how your employer knows enough about your tax situation to not significantly over or under withhold. If my wife and I just relied on the basic IRS calculations on the W-4 and didn't specify additional withholding by dollar amount we would end up owing thousands, possibly over $10,000, the following April (before penalties). How do Ireland and others avoid that?