  Let \Gamma(n,p) denote the binomial model of a random triangular group. We
show that there exist constants c, C > 0 such that if p <= c/n^2, then a.a.s.
\Gamma(n,p) is free and if p >= C log n/n^2 then a.a.s. \Gamma(n,p) has
Kazhdan's property (T). Furthermore, we show that there exist constants C',c' >
0 such that if C'/n^2 <= p <= c' log n/n^2, then a.a.s. \Gamma(n,p) is neither
free nor has Kazhdan's property (T).
