We study the distribution of stars , HII regions , molecular gas , and individual giant molecular clouds in M33 over a wide range of spatial scales .
The clustering strength of these components is systematically estimated through the fractal dimension .
We find scale-free behavior at small spatial scales and a transition to a larger correlation dimension ( consistent with a nearly uniform distribution ) at larger scales .
The transition region lies in the range \sim 500 - 1000 pc .
This transition defines a characteristic size that separates the regime of small-scale turbulent motion from that of large-scale galactic dynamics .
At small spatial scales , bright young stars and molecular gas are distributed with nearly the same three-dimensional fractal dimension ( D _ { f, { 3 D } } \lesssim 1.9 ) , whereas fainter stars and HII regions exhibit higher values D _ { f, { 3 D } } \simeq 2.2 - 2.5 .
Our results indicate that the interstellar medium in M33 is on average more fragmented and irregular than in the Milky Way .