A positron will lose its kinetic energy through ionizations and excitations in a similar fashion to a negative beta particle. However, the positron will then combine with an electron. The two particles are annihilated, producing two 511 keV photons called annihilation radiation . Both are electromagnetic radiation, and differ only from radio waves and visible light in having much shorter wavelengths. They have zero rest mass and travel with the speed of light.
Photons have no definite maximum range.
However, the total fraction of photons passing through an absorber decreases exponentially with the thickness of the absorber. The electrons from ionizations and pair production will themselves go on to cause more ionization and excitation events in the same way as described for betas.