So you are asking if jQuery is in the public domain or not, right? If so, for details see:
http://docs.jquery.com/Licensing
I and many others find these licensing statements quite confusing though. So I would say that as far as I know jQuery is free for public (personal or commercial) use as long as you indicate in your source code that it is being used, and that any modifications to it that you make as well as any specific applications you put it to (whether code you write or code you found elsewhere) are publicly available to any and all that may find them in your source code and want to use them or develop them further. However, under certain curcumstances you might (or might not) be permitted to charge others for your work that uses jQuery.
Put more simply, jQuery is free, as long as you don't charge for it, which is generally not allowed. If you have need of a different relationship to the jQuery script library, a careful reading of the Licensing terms may reveal an approach that suits you.
If I misunderstood, and you have a different question, please be more clear as to what it is.
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