teem (1) Look up teem at Dictionary.com
"abound, swarm," O.E. teman (Mercian), tieman (W.Saxon) "give birth to, produce," from P.Gmc. *taumijanan, from PIE *deuk- "to lead" (see duke). Related to team in its now-obsolete O.E. sense of "family, brood of young animals." The meaning "be fertile, abound, swarm" is first recorded 1593; teeming in this sense is from 1715.
teem (2) Look up teem at Dictionary.com
"to flow copiously," c.1300, from O.N. toema "to empty," from tomr "empty," cognate with O.E. tom "empty." The original notion is of "to empty a vessel," thus "to pour out."