"abound, swarm," Old English teman (Mercian), tieman (West Saxon) "give birth to, produce," from Proto-Germanic *taumijanan, from PIE *deuk- "to lead" (see duke (n.)). Related to team in its now-obsolete Old English sense of "family, brood of young animals." The meaning "be fertile, abound, swarm" is first recorded 1590s. Related: Teemed; teeming.
"to flow copiously," c.1300, from Old Norse toema "to empty," from tomr "empty," cognate with Old English tom "empty." The original notion is of "to empty a vessel," thus "to pour out." Related: Teemed; teeming.