In my experience (YMMV), the limit is 3 times the maximum out at one time, and it's enforced for the patron's chosen checkout duration.
For example, if a library allows 5 books out at one time, and you check out your first book January 1 at noon, the error occurs if you try to check out a 16th book before January 8 at noon (if your loans are set for a week at a time).
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