How big can the universe's first starbursts get?

As our telescopes have improved and we've been able to peer farther back in time, we've begun finding more fascinating features of the universe. But one thing we haven't found for sure is Population III (Pop III) stars. These were the earliest stars in the universe, formed completely from pristine hydrogen and helium, with no "metals" (i.e., elements heavier than those two) polluting their processes.