Jon Gosselin, Kate Gosselin

Jon Gosselin brought flowers for Kate during their divorce arbitration, but his estranged wife wanted nothing to do with his so-called "peace offering."

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"This has been called the real-life War of the Roses," Jon's attorney Mark Heller told People, "and he brought that as a peace offering to break the ice and try to bring the war to an end."

But Kate, also present at the daylong divorce arbitration hearing on Saturday, turned them down.

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According to Heller, the arbitrator is expected to rule in a month, and the divorce could be finalized by the end of the year.

During the arbitration, custody, child support and distribution of assets were addressed.

"There were a couple of very emotional moments," said Heller, "but in the end it all came together and concluded on a happy note."

Monday marks the finale of TLC's Jon & Kate Plus 8.