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If you already have another TeX distribution (like MacTeX-2012), it is not necessary to remove that distribution before installing MacTeX-2013. The old distribution will remain after installation and you can easily switch back to it if you discover a flaw in TeX Live 2013. A "TeX Distribution Preference Pane" has been added to Apple's System Preferences; this pane lists installed TeX distributions and allows you to select the active distribution by clicking a radio button in the pane. This click automatically reconfigures all TeX GUI applications, and automatically reconfigures the PATH and MANPATH variables. See the documentation on Multiple TeX Distributions below for details.
If you want to remove your old distribution after installing MacTeX-2013, read the document on "Uninstalling".
For a list of new features in MacTeX-2013, click here.