Completions of UFDs with semi-local formal fibers

Let ( T , M ) be a complete local ring such that | T / M | = | T |. Given a finite set of incomparable nonmaximal prime ideals C of T , we provide necessary and sufficient conditions for T to be the completion of a local UFD A , whose generic formal fiber is semilocal with maximal ideals the elements of C . We also show that, given the T above, we can find necessary and sufficient conditions for T to be the completion of a UFD, whose formal fiber over a height one prime ideal is semilocal.