  The phase diagram of 2d Lorentzian quantum gravity (LQG) coupled to conformal
matter is studied. A phase transition is observed at $c=c_{\rm crit}$
($1/2<c_{\rm crit}<4$) which can be thought of as the analogue of the $c=1$
barrier of Euclidean quantum gravity (EQG). The non--trivial properties of the
quantum geometry are discussed.
