  In this paper we perform the calculation of the spectral dimension of the
space-time in 3d quantum gravity using the dynamics of the Ponzano-Regge vertex
(PR) and its quantum group generalization (Turaev-Viro model (TV)). We realize
this considering a very simple decomposition of the 3d space-time and
introducing a boundary state which selects a classical geometry on the
boundary. We obtain that the spectral dimension of the space-time runs from 2
to 3, across a 1.5 phase, when the energy of a probe scalar field decreases
from high to low energy. For the TV model the spectral dimension at hight
energy increase with the value of the cosmological constant. At low energy the
presence of the cosmological constant does not change the spectral dimension.
