Kardashian appeared by video for the downtown Los Angeles court hearing Wednesday. Ye did not attend, but his attorney was present and did not object to the dissolution of the marriage while financial and child-custody issues still remain pending.
Kardashian filed for divorce more than a year ago, but the case has languished over the complex financial issues and the pair worked out custody of their four children.
But Kardashian -- who has been publicly dating "Saturday Night Live" cast member Pete Davidson since October -- filed court papers late last year asking a judge to expedite the divorce, even as those other issues remain unresolved.
West objected in court papers of his own, with his attorneys making a series of technical objections to Kardashian's bid to have the pair declared legally single. The attorneys argued that several issues need to be resolved before the pair can be declared officially divorced, such as protection of joint trusts or financial accounts, even though the pair did sign a prenuptial agreement.
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Judge Steven Cochran granted one of the conditions regarding the handling of financial matters in the event either of them die before the divorce is finalized.
Ye has been publicly vocal about his interest in reconciling with Kardashian. But both of them have been seen dating other people in recent months.
In papers filed last month in support of her bid to end the marriage, Kardashian wrote, "I very much desire to be divorced."
"I have asked Kanye to keep our divorce private, but he has not done so," Kardashian claimed in the declaration. "I believe that the court terminating our marital status will help Kanye to accept that our marital relationship is over and to move forward on a better path which will assist us in peacefully co-parenting our children."
She added, "While I wish our marriage would have succeeded, I have come to the realization that there is no way to repair our marriage. Kanye does not agree but at least it appears that he has come to the realization that I want to end our marriage, even if he does not."
The couple have been married since mid-2014, and they have four children.
The divorce is the third for Kardashian, but the first for Ye.
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