The End of the Affair? Not for Eric Schmidt.

While Mr. Schmidt was chief executive of Google, he had an extramarital relationship with Marcy Simon, a public relations executive. A decade after they split, things are still messy.

When Eric Schmidt was the chief executive of Google in the mid-2000s, he dated Marcy Simon, a New York-based public relations executive. Both were married to other people at the time.

Mr. Schmidt and Ms. Simon were seen together on the French Riviera, at tech conferences and on Fire Island, where she owned a beach house. When a large yellow diamond ring was spotted on Ms. Simon’s finger, some speculated in the media that Mr. Schmidt might divorce his wife and marry Ms. Simon.

But Mr. Schmidt moved on to other girlfriends. Although he and Ms. Simon, who divorced her husband, later rekindled their relationship in the late 2000s and early 2010s, they decided to go their separate ways in 2014, people with knowledge of their relationship said.

For billionaires, and the people who love them, breaking up can be a little like unraveling a corporate merger gone wrong. Ending Mr. Schmidt’s affair has taken a decade — so far. There have been contracts, amended contracts, arbitrations, lawsuits and the platoon of advisers that inevitably go along with all that.

Mr. Schmidt, now 69 years old, approved a confidential settlement in 2014 with Ms. Simon that paid her an undisclosed amount of money, and appointed an adviser, Derek Rundell, to set it up. Under the arrangement, Ms. Simon would bring Mr. Schmidt investment ideas that Mr. Rundell would evaluate on his behalf.

But the deal imploded when Ms. Simon and Mr. Rundell fought bitterly, leading to years of wrangling that culminated in accusations of fraud against Ms. Simon last year over an investment in the luggage maker Away. Ms. Simon has denied committing fraud.