Most of these libraries take one of the following approach in their implementation:
b. Creating wrapper object/function to expose various utility functions
c. Combination of approach (a) and (b)
Libraries like prorotype.js extend native object alot, where as, jQuery is into wrapper object.
Where as, when a wrapper object or function is created, then utility functions are associated and exposed to this particular wrapper in various manners, like $ in jQuery.
Both the approaches have their pros-cons.
If planning to create your own utility library, its great to keep these approaches in mind and choose the one you feel suits the vision of your library in the long run.