While President Trump and Joe Biden fought to be heard in a rowdy debate Tuesday, both campaigns sought to draw digital battle lines and occupy online turf they could have all to themselves.

The big picture: Trump's impulsive Twitter style made a shambles of the debate format, but online the candidates were able to find niches where they couldn't be interrupted — and could motivate their supporters to donate, organize and turn out to vote.

Tuesday night, both candidates were all over social and traditional media, as expected, but each managed to find some unique ground.

• Trump bought a takeover ad that dominated the home page of YouTube, ensuring his message was the first one seen by those who headed to the Google-owned video site, whether they were there to watch the debate or seek respite from it.
• Joe Biden, meanwhile, nabbed the Twitter account "@truth" and used it to fact check during and after the debate.

Of note: One of the debate's key moments, in which Trump refused to condemn white supremacists, had immediate online repercussions. The president's statement that the far-right Proud Boys group should "stand down and stand by" was instantly embraced as a rallying cry.

• “President Trump told the proud boys to stand by because someone needs to deal with ANTIFA...well sir! we’re ready!!” Proud Boys organizer Joe Biggs wrote on conservative social media platform Parler. “Trump basically said to go fuck them up! this makes me so happy.”
• The public Proud Boys account on messaging platform Telegram turned Trump’s “Stand back … stand by” command into a logo immediately after the debate.

Between the lines: Both sides will use the words from the debate, loud and interrupted as they were, to fundraise. The Trump campaign, however, jumped the gun a bit, sending out a post-debate pitch declaring an on-stage victory hours before the debate took place, reminiscent of a similar gaffe in 2016.

Meanwhile: In the hours before the debate, a baseless conspiracy theory that Joe Biden would wear an electronic device in his ear during the debate went viral on social media.

• The conspiracy originated on social media before appearing in a text message sent by Trump’s campaign to supporters. It was then regurgitated by media outlets like Fox News and New York Post, who cited the Trump campaign, throughout the day, according to NBC News.
• One particular meme was simultaneously posted by multiple Facebook pages with names like “US Conservative” and “The Unhinged Left” and received thousands of shares, according to NBC.
• Kate Bedingfield, communications director for the Biden campaign, called the rumor “completely absurd” during a call with reporters on Tuesday.
• Biden, meanwhile, poked fun at the issue on social media.

Why it matters: It's just the latest example of how false information that gains traction on social media can then enter the national conversation when it's amplified first by partisan media and then by the mainstream press.

Our thought bubble: With its constant interruptions, its inability to obey its own rules, and the failure of its moderator to maintain order, the debate looked a lot like social media at its worst. Twitter, by comparison, looked almost civil.