  We investigate the phase diagram of non-perturbative three-dimensional
Lorentzian quantum gravity with the help of Monte Carlo simulations. The system
has a first-order phase transition at a critical value $k_0^c$ of the bare
inverse gravitational coupling constant $k_0$. For $k_0 > k_0^c$ the system
reduces to a product of uncorrelated Euclidean 2d gravity models and has no
intrinsic interest as a model of 3d gravity. For $k_0 < k_0^c$, extended
three-dimensional geometries dominate the functional integral despite the fact
that we perform a sum over geometries and no particular background is
distinguished at the outset. Furthermore, all systems with $k_0 < k_0^c$ have
the same continuum limit. A different choice of $k_0$ corresponds merely to a
redefinition of the overall length scale.
