I was using two other software products to do what MacPARdeluxe does in one shot.
With its simple to use interface, you simply click on the very prominent "open" button
at the top left corner of the MacPARdeluxe window.

When the "choose selection" window opens, it usually finds the appropriate PAR file needed,
or you simply select it manually.

The program does the rest, quickly and clearly showing you its progress
in a fresh MacPARdeluxe window which opens automatically (saving you
the hassle of clearing a window should you be processing multiple PAR files.)

MPD analyzes your PAR files, restores whatever files are necessary
and lets you know when it is finished. In most cases it unPARs as well,
producing a finished file ready to use. In those few cases where
it restores your broken files but doesn't decode them automatically,
simply use Ajoiner or a similar program to finish up.

NOTE: MPD is defaulted to auto-trash some of your PAR bits as it uses them.
If you want to save the entire PAR set, you need to change this function
in the program's preferences.

MacPARdeluxe is the FIRST program you should try if getting into PAR extraction.
It does the job right (at least in 10.3.9) and is very fast and extremely reliable.

Thank you, Mr. Putter!