  In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest
degree of the splitting. We prove sharp upper and lower bounds for the rank in
the case $k=1$ and moreover we give families of examples for every allowed
possible rank and explain which relation exists between the families. After
dealing with the case $k$ in general, we conjecture that every $k$-type uniform
Steiner bundle is obtained through the proposed construction technique.
