Kimora and Russell Simmons, in 2005
03/26/2008 AT 08:00 PM EDT
Kimora Lee Simmons filed for divorce from her estranged husband, Russell Simmons, in Los Angeles County Superior Court Tuesday.
The couple announced that they had split up
in March 2006, but said they had already been separated "for some time."
In court papers, Kimora, 32, cites irreconcilable differences and asks for legal and physical custody of the couple's two daughters, Ming, 8, and Aoki, 5. She requests that Simmons, 50, get "reasonable child visitation … to be accompanied at all times by the children's nanny and security personnel.
At the time of their initial separation in 2006, Simmons said in a statement: "Kimora and I will remain committed parents and caring friends with great love and admiration for each other."
Kimora has been dogged recently by rumors that she is expecting a child with boyfriend Djimon Hounsou. At an appearance in Chicago earlier this month, she told reporters
. "I'm in the paper every single week – that I had a fight with my ex-husband, or that I was mad at one of his girlfriends, or that I'm pregnant, or that I demand Fiji water … Lies upon lies upon lies."