  Two-dimensional random Lorentz gases with absorbing traps are considered in
which a moving point particle undergoes elastic collisions on hard disks and
annihilates when reaching a trap. In systems of finite spatial extension, the
asymptotic decay of the survival probability is exponential and characterized
by an escape rate, which can be related to the average positive Lyapunov
exponent and to the dimension of the fractal repeller of the system. For
infinite systems, the survival probability obeys a stretched exponential law of
the form P(c,t)~exp(-Ct^{1/2}). The transition between the two regimes is
studied and we show that, for a given trap density, the non-integer dimension
of the fractal repeller increases with the system size to finally reach the
integer dimension of the phase space. Nevertheless, the repeller remains
fractal. We determine the special scaling properties of this fractal.
