A fetal transfer is a process in which a fetus is transferred from one womb to another.
According to USS Baldwin captain Patrick Ingrum, the procedure made elective abortions obsolete. He also indicated that the physician who performed the first fetal transfer received two Nobel prizes. (USS Baldwin: "Mother and Child")
In late 2373, a fetus was removed from Jaimie Petrelli without her consent. Jaimie did not know about it - nor did she know she was ever pregnant to begin with - until 2378, when the child, named Joshua, was discovered on Salva II as a slave of the Orion Syndicate. (USS Baldwin: "Mother and Child")
Around Stardate 49930.3, Keiko O'Brien, who was pregnant with her second child, was critically injured. To save the fetus, Dr. Bashir had to transfer him into the womb of Kira Nerys. Due to a significant difference between Human and Bajoran gestation, Kira had to carry the child to term. (DS9: "Body Parts")
For the USS Baldwin episode "Mother and Child," writer Richie Kennedy takes the concept and suggests possible good (the concept of using the fetal transfer in lieu of an abortion) and a possible evil (kidnapping a fetus in utero without the mother's knowledge)