It would depend exactly on how and when Trump went independent. If it became obvious early on (say after the 2022 midterms) that Trump wasn't going to get chosen by the Republicans and he went independent at that point, it'd probably have a similar outcome to Theodore Roosevelt's third-party run in 1912 - he wouldn't win, but he'd probably beat the Republican candidate down into the third place.
However, if he lost in the primaries, that would be a different story, as a lot of states have "sore loser" laws which prohibit people from running as independents if they lose a major party's nomination. In that case, Trump wouldn't be on the ballots in enough states to have any major effect on the election.







