The judge overseeing Jennifer Lopez and Ben Affleck's messy and complicated divorce has a family connection to both celebs, plus one of J Lo's famous exes ... but he's shrugging off concerns of a possible conflict of interest.

It's really incredible -- and just goes to illustrate Hollywood's tangled web -- but the judge assigned to Bennifer's divorce, Bradley S. Phillips, has a son-in-law who freaking works as an agent for not only Ben, but also Alex Rodriguez!!!

In new legal docs, obtained by TMZ, Judge Phillips discloses his son-in-law is Strand Conover ... a partner and agent at WME, the talent agency that reps both Ben and A-Rod.

This goes even deeper, though ... Strand not only works at WME ... he's a member of the team representing Ben ... and Judge Philips says Strand knows J Lo through his work with Ben.

In another strange twist, Judge Phillips says Strand is also WME's brand-partnership agent for A-Rod ... and he's met J Lo through business dealings with her former fiancé too.

So, the judge's son-in-law knows Ben and J Lo pretty well ... though he's never repped Jen.

On its face, it seems like there's a possible conflict of interest here, but Judge Phillips is shrugging his shoulders ... the judge says he doesn't believe his son-in-law's connections to Bennifer will affect his ability to be fair and impartial.

Judge Phillips says he hasn't talked to his son-in-law about Bennifer or their divorce ... and won't do so as the case moves forward. Strand's gotta be happy -- less time with his in-laws!!!