"endlessly," Latin, literally "to infinity" from ad "to, unto" (see ad-) + infinitum "infinity," neuter accusative of adjective infinitus "endless" (see infinite). English version to infinity is attested from 1630s.
talked on and on ad infinitum
ad-
*ad-
-ad
ad hoc
ad hominem
ad infinitum
ad lib
ad nauseam
ad valorem
Ada
adage