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API as in a series of commands you can send to any XOOPS site that automagically regsiters a user for that XOOPS website? That kind of API? There isn't one, other then the form used for registration. Fill in those fields and submit the form.
There's a reason for this tho (besides the simple fact that no-one ever built it): registration thru an API could bring a lot of unwanted user registrations, if not dealt with carefully. Users=access rights, and an increased security risk.
Herko