Kid Cudi Gives Up Custody Battle -- You Can Keep Our Daughter

Kid Cudi's waving the white flag in his bitter custody dispute with his baby mama -- agreeing to let his baby mama take full custody of their daughter ... TMZ has learned.

The custody war has been quietly raging on for over a year -- with Cudi and his baby mama arguing back and forth over who should get full custody.

Cudi said he got a place in Chicago just to be close to his daughter and her mother -- and provided his daughter with generous support -- but his baby mom said that was BS, insisting Cudi was provided "sporadic and inconsistent amounts" of support ... and was an absentee dad.

In court docs, she also claimed Cudi has violent tendencies and a "long history of consistent drug and alcohol abuse."

The two parties finally agreed to disagree on August 3rd -- and Cudi let his baby mama take full custody.

In return, she agreed to let him have visitation. Cudi will also pay child support.