Nikki Bella Asks for Legal & Physical Custody of Son in Divorce Docs

Nikki Bella wants to keep her son with her ... asking for legal and physical custody of her son Matteo in her divorce from Artem Chigvintsev.

The former WWE star cites irreconcilable differences in the dissolution docs ... citing August 29 as the date of separation, the day Artem was arrested for felony corporal injury to a spouse or cohabitant.

Bella checked the box to block the court's ability to award spousal support to either of them.

As for their son, Matteo, who turned 4 in July ... Nikki wants legal and physical custody, but is open to Artem getting visitation rights.

As we told you ... Artem originally called 911 at the end of August to request medical assistance for the alleged victim ... only to call paramedics off minutes later. Cops still showed up and arrested him.

Formal charges have not yet been brought against Artem for the incident ... though we're told investigators turned the case over to prosecutors last week.

We also told you Nikki filed for divorce yesterday ... not exactly a surprise given she's ditched her wedding ring in recent days -- filming the Chestnut vs. Kobayashi hotdog-eating contest sans ring days after the incident.