Anyone holding out hope that Kim Zolciak and Kroy Biermann might find some common ground during their nasty divorce should just give up ... cuz it just ain't happening.
Sources with direct knowledge tell us the estranged couple has stopped all direct communication ... only having a back and forth using their lawyers.
What's more -- the two still live under the same roof, but in separate wings of the house, while still sharing their 4 young kids between the two of them. Our sources says there's absolutely zero chance the pair will ever get along again, things are just that bad.
When speaking of their relationship, our source says, "They hate each other. It's very contentious." We're told the whole thing has been messy for their family, and will continue at least until the divorce is finalized and Kim and Kroy can legally go their separate ways.
TMZ broke the story, Kim filed docs earlier this week defending herself as a mother and accusing Kroy of being mentally and emotionally abusive over the years.
Kroy's taken his own jabs at Kim, too, accusing her of having a serious gambling addiction and asking the judge for sole physical and legal custody of the couple's children.
Of course, the divorce has been nasty from the beginning ... both filed separate divorce petitions on the heels of TMZ learning the couple is in the hole with the IRS for more than $1 million.