  We study properties of dilute polymer solutions which are known to depend
strongly on polymer elongation. The probability density function (PDF) of
polymer end-to-end extensions $R$ in turbulent flows is examined. We
demonstrate that if the value of the Lyapunov exponent $\lambda$ is smaller
than the inverse molecular relaxation time $1/\tau$ then the PDF has a strong
peak at the equilibrium size $R_0$ and a power tail at $R\gg R_0$. This
confirms and extends the results of \cite{Lumley72}. There is no essential
influence of polymers on the flow in the regime $\lambda\tau<1$. At
$\lambda>1/\tau$ the majority of molecules is stretched to the linear size
$R_{\rm op}\gg R_0$. The value of $R_{\rm op}$ can be much smaller than the
maximal length of the molecules because of back reaction of the polymers on the
flow, which suppresses velocity gradients thus preventing the polymers from
maximal possible stretching.
