  Braneworld models are interesting theoretical and phenomenological frameworks
to search for new physics beyond the standard model of particles and cosmology.
In this work, we discuss braneworld models whose gravitational dynamics are
governed by teleparallel $f(T)$ gravities. Here, we emphasize a codimension two
axisymmetric model, also known as a string-like brane. Likewise, in the 5D
domain-walls models, the $f(T)$ gravitational modification leads to a phase
transition on the perfect fluid source providing a brane-splitting mechanism.
Furthermore, the torsion changes the gravitational perturbations. The torsion
produces new potential wells inside the brane core leading to a massless mode
more localized around the ring structures. In addition, the torsion keeps a
gapless non-localizable and a stable tower of massive modes in the bulk.
