Let $T$ be a complete equicharacteristic local (Noetherian) UFD of dimension $3$ or greater. Assuming that $|T| = |T/\mathfrak m|$, where $\mathfrak m$ is the maximal ideal of $T$, we construct a local UFD $A$ whose completion is $T$ and whose formal fibers at height one prime ideals have prescribed dimension between zero and the dimension of the generic formal fiber. If, in addition, $T$ is regular and has characteristic zero, we can construct $A$ to be excellent.
"Completely controlling the dimensions of formal fiber rings at prime ideals of small height." J. Commut. Algebra 11 (3) 363 - 388, 2019. https://doi.org/10.1216/JCA-2019-11-3-363