By JJ: To assist Hugo nominators, listed below are the series believed to be eligible as of this writing for the 2021 Best Series Hugo next year *†.
Each series name is followed by the main author name(s) and the 2020-published work(s).
Feel free to add missing series and the name of the 2020-eligible work in the comments, and I will get them included in the main post.
I just ask that suggesters (1) first do a Find on author surname on this page, to check whether the series is already on the list, and (2) then make an effort to verify that a series does indeed have 3 volumes, that it has a 2020-published work, and that it has likely met the 240,000 word threshold. Self-published works may or may not be added to the list at my discretion.
Note that previous Hugo Administrators ruled that nominations for a series and one of its subseries will not be combined. Therefore, when nominating a subseries work, think carefully under which series name it should be nominated. If the subseries does not yet meet the 3-volume, 240,000 word count threshold, then the main series name should be nominated. If the subseries does meet that threshold, then the subseries name should probably be nominated. This will ensure that another subseries in the same universe, or the main series itself, would still be eligible next year if this subseries is a finalist this year.
* ineligible series are preceded by an asterisk