12:26 PM PT -- Authorities have identified the man who set himself on fire as Maxwell Azzarello -- and they say he arrived in New York at some point over the past week. They say he walked into the park, threw pamphlets onto the ground and then doused himself in some kind of substance.

He then lit himself on fire, and is now at a burn unit in critical condition. Fire officials say his family was unaware he was even in New York -- apparently, the guy came from Florida.

A man set himself on fire in front of the courthouse where former President Donald Trump's hush money criminal trial is currently underway ... and the footage is shocking.

Pictures and videos of the unidentified man spread all over social media Friday -- this as jury selection was wrapping in an NYC courtroom, where Trump is on trial. As you can see, it was absolutely shocking to all those around ... as the guy was completely engulfed in flames.

The video is disturbing ... catching the man writhing on the ground as he's very badly burned. Authorities rushed to put out the flames with a fire extinguisher, and it took some time to put out the inferno. Cops tell TMZ the male was transported to a hospital in critical condition.

Not only did passersby film the horrific moment ... but, several news stations caught it as well during their live shots -- who were on hand to report on Trump, interrupting their broadcast.

CNN, for example, was in the middle of a live report ... and filmed the beginnings of the fire before cutting away to its anchors who instead described the scene for the audience, with rapid-fire stream of consciousness details.

Just as dramatic as the fire was, the reporter's flurry of intel was just as wild, especially as it played out on TV.

We don't yet know if this man's self-immolation had anything to do with the Trump trial itself, but the former Prez's criminal case is certainly a hot-button issue for many Americans.

Donald's facing 34 state counts of falsifying business records for allegedly having his lawyer pay porn star Stormy Daniels hush money in the run-up to the 2016 election.

The trial began Monday ... and, now, all jurors have been seated with Opening Statements set for Monday. Unclear if proceedings were affected by the incident outside the courthouse ... or if Trump himself was aware of it or not.