  We study the three-boson bound-state mass and wave functions for ground and
excited states within the three-body relativistic framework with Kamada and
Gl\"ocke boosted potentials in the limit of a zero-range interaction.
  We adopt a nonrelativistic short-range separable potential, with Yamaguchi
and Gaussian form factors, and drive them towards the zero-range limit by
letting the form factors' momentum scales go to large values while keeping the
two-body binding fixed. We show that the three-boson relativistic masses and
wave functions are model-independent towards the zero-range limit, and the
Thomas collapse is avoided, while the nonrelativistic limit kept the Efimov
effect. Furthermore, the stability in the zero-range limit is a result of the
reduction of boosted potential with the increase of the virtual pair center of
mass momentum within the three-boson system. Finally, we compare the present
results with Light-Front and Euclidean calculations.
