  We deal with a random graph model evolving in discrete time steps by
duplicating and deleting the edges of randomly chosen vertices. We prove the
existence of an a.s. asymptotic degree distribution, with streched exponential
decay; more precisely, the proportion of vertices of degree $d$ tends to some
positive number $c_d>0$ almost surely as the number of steps goes to infinity,
and $c_d\sim (e\pi)^{1/2} d^{1/4} e^{-2\sqrt d}$ holds as $d\to\infty$.
