Because I should indulge in fantasy NYS politics before the polls close -
(and I may have made mistakes, lacking a complete election law guide, but...)
In New York, 50,000 votes on a party's line for Governor ensure that party has official status - people can register for that party, the party has control over the name and logo, and so on. The two parties that get the most votes get lines A and B, plus ALL OF THE PATRONAGE JOBS AT THE BOARDS OF ELECTIONS in the state. The others lines are assigned by numbers of votes, but have minimal or no patronage.
Usually that's the Democrats and the Republicans. The patronage splits almost equally, and those are the only parties that have held those lines in a long while, so it's been very stable.
If Zephyr Teachout wins today's Democratic primary for Governor, Cuomo is still on the ballot - Independence, Working Families, and Women's Equality Party. Rob Astorino has the Republican and Conservative lines. Howie Hawkins has the Green Party line.
The Conservatives are probably fine. Their core voters will vote the line anyway, so I'd be be very surprised if anything happened to their ballot status.
The Green Party has won 50,000+ votes for a while, since "Grampa Al" Munster I mean Lewis helped them cross the threshold. A lot of voters who keep them there would have a hard choice to make if Teachout is the Democratic nominee. Howie Hawkins is not an attorney, and I don't think the Greens have an easy way to nominate him for a judgeship, so I don't think they could replace him with Teachout on the ballot. It's conceivable _though unlikely_ that the Greens could lose their official ballot status.
The Republican Party would have a new challenge: making sure Astorino came in second and not third, and with enough of those votes on the Republican rather than Conservative line to maintain Line B. It's also conceivable that Teachout and Cuomo destroy each other and Astorino wins, getting the Republicans Line A. However, I suspect that too large a chunk of Republicans would prefer Cuomo to Astorino to make that anything like a safe bet.
The Independence and Working Families Parties would probably both be fine as far as ballot status, but there would be a very strange scramble between them to try to get line A or B. I have no real idea how that would work out - perhaps the one that promises to be most Cuomonian would get the nod.
(The Women's Equality Party is currently a figment of Cuomo's imagination. Cuomo could pour everything into that line and make it a party.)
The Democrats would face another challenge. The NYS Democratic Committee suddenly won't be able to help Cuomo, at least not directly. Would they switch to wholeheartedly support Teachout? Would the patronage employees fight to make sure she got at least line B? If she came in third, behind Cuomo and Astorino, the Democratic patronage machine would vanish for four long years.
Odds on all of these are small, but it's possible this year to imagine either the Democrats or the Republicans losing their top line ballot status and patronage positions. That's a first in a long while.
If Tim Wu wins today's Democratic primary for Governor, and Teachout doesn't, then the Independence Party and Working Families Party have to fear for their ballot existence. (The Republicans, Greens, and Conservatives are fine.)
On the Election Day ballot, the Governor and Lieutenant Governor run as a single line. Votes only accumulate if both names on the line are the same across parties. Votes for Cuomo/Wu don't add up with votes for Cuomo/Hochul, and effectively the Cuomo/Hochul votes would be discarded.
Theoretically, Kathy Hochul could be nominated for a judgeship, removed from the ballot, and replaced with Wu. That seems to require Wu's consent however, and he's already said that he wouldn't mind killing the Independence Party. He's not in a mood to cooperate with Cuomo, and the WFP rejected Teachout earlier, so it's conceivable that the Independence, WFP, and Women's Equality Parties would be stuck with a dud ballot.
If that happens, the WFP would probably be in the strongest position to hold its line with pointless ballots, as they have a voter turnout machine already in place. I don't know what would happen if Cuomo/Astorino became a close race.
I'm not sure what the Independence Party could do to promote itself in that situation. They're kind of the middle party without a personality, or with multiple personalities, and haven't built a strong operation that I'm aware of. Wu's refusal to take their line might well cost them their ballot status.
Teachout winning and Wu losing to Hochul doesn't create additional chaos beyond Teachout winning that I can see.
I'll leave this up here whatever the results of the race because it's been an interesting exercise, showing what's at stake beyond the obvious questions of who runs New York State. A lot of this is doubtless wishful thinking, but may become more important in future races.