  We prove that for random affine code tree fractals the affinity dimension is
almost surely equal to the unique zero of the pressure function. As a
consequence, we show that the Hausdorff, packing and box counting dimensions of
such systems are equal to the zero of the pressure. In particular, we do not
presume the validity of the Falconer-Sloan condition or any other additional
assumptions which have been essential in all the previously known results.
