What is the effect of the master manumitting a Mukataba on her child's status?

Primary text

Ahmad, Sufyan, and Ishaq are of the opinion that if a Mukataba pays her stipulated amount or is manumitted, her child is manumitted. Conversely, if the Umm Walad or the Mudabbara is manumitted, her child is not freed until the master dies. The apparent meaning is that the child of the Mukataba follows her in manumission upon the master's freeing her, as the child's earnings are part of her estate, thus following her when she is freed like her property. Moreover, freeing the Mukataba prevents the master from receiving the payment for her manumission, which resembles the master absolving her of the obligation of the writing of manumission (Kitaba).