10:45 AM PT -- Sources connected to the litigation tell TMZ months ago a judge suspended Rob's entire obligation to pay any child support until he could evaluate Chyna's resources as well as Rob's, so for now, Chyna's getting $0 in child support.

Rob Kardashian has gone into court to get a reduction in child support, but it's something he planned on doing for more than a year ... and it was all designed to get Blac Chyna to drop domestic violence allegations that could have cost him custody.

Sources connected to the case tell TMZ, Rob and Chyna are now locked in a war over how much he has to pay to support 2-year-old Dream. As we reported, Rob agreed in September 2017 to pay her $20,000 a month in child support. He now says he's basically broke and she's rolling in the dough.

Our sources say, Rob agreed to pay $20k a month knowing that a judge would have reduced that amount significantly, but he needed Chyna to back off her claim he physically abused her -- aggressively hitting, shoving and pushing her to the ground during their relationship -- something that could have badly hurt him in their custody fight.

In return for Rob agreeing to pay $20k a month, Chyna dropped her domestic violence restraining order and agreed to give him 50/50 joint custody of their child. Our sources say Rob planned from the get-go to let some time pass, then go back into court and ask for a reduction in child support, claiming he has virtually no income. That's exactly what he has done.

Chyna's lawyer, Lisa Bloom, tells TMZ ...Chyna was NOT played and she knew Rob would probably go back into court for a reduction in support. Bloom says her client made her point and got what she wanted -- an agreement Rob would leave her alone. She also got him to agree not to post more revenge porn targeting her, something Bloom says has dogged Chyna to this day.

Bloom says Chyna never wanted to fight over custody and wanted Rob to be involved in Dream's life. She also claims Rob is pretending to be poor when he leads a lavish lifestyle. She says, "Rob has deliberately retreated from social media to suppress his income in order to reduce support. What kind of father plays games with supporting his own baby?"

And, Bloom says, Chyna still has a separate, active civil case against Rob which raises the domestic violence issue.