Should pagination be centered?
Exactly, pagination controls should go where they fit logically on a page, that isn't always going to be in the center, in the left or in the right.
Should pagination be on left or right?
Pagination: Page numbers should be placed in the top margin one inch from the right side of the paper. The number should appear by itself with no punctuation.
Why should we avoid pagination?
Some paginations can have so many pages that the page numbers start to reach triple digits. No user will ever sit and browse from page 1 to 100. This is why you should never display your content as a giant, endless archive.