  The ground-state and the transport properties of graphene subject to the
potential of in-plane charged impurities are studied. The screening of the
impurity potential is shown to be nonlinear, producing a fractal structure of
electron and hole puddles. Statistical properties of this density distribution
as well as the charge compressibility of the system are calculated in the
leading-log approximation. The conductivity depends logarithmically on
$\alpha$, the dimensionless strength of the Coulomb interaction. The theory is
asymptotically exact when $\alpha$ is small, which is the case for graphene on
a substrate with a high dielectric constant.
