Eek, sorry. I should have said, a couple years after the breakup.
But yeah, right during the breakup, it was that she was cheating with Ewan McGregor on the set of Moulin Rouge, which was amplified by Tom's "Nicole knows" schtick and the general belief at the time that they had adopted because Nicole couldn't get pregnant, so a miscarriage made sense and would explain why there was no baby if she had had an affair and gotten pregnant. You're right, it was everywhere. I think Ewan McGregor even refused to go on Letterman ever again because Dave implied he was having an affair on-air.
But if I'm not misremembering again, one of the scieno tell-alls that came out a short while later, before Tom went demonstrably crazy, said that the "Nicole knows" thing was about Scientology, not about an affair, and that Tom dumped Nicole right before the ten year mark because the Church leaders told him she was a suppressive. And then everyone was all, "Hmmmm, I guess it's possible." And then Tom went nuts, and it was like, "Oh, so I guess that is what really happened."
I'm keeping my fingers crossed that I didn't totally screw up the timeline this time.