Diffusion-controlled scavenging of mobile holes under no applied electric field was observed directly in poly(N-vinylcarbazole) films, doped with 1,2,4,5-tetracyanobenzene (TCNB) as an electron acceptor and N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) as a hole scavenger, by transient absorption spectroscopy. The scavenging of holes occurs mainly over several nanoseconds, and is complete within 1 mu s. The mean diffusion length of the migrating holes was estimated to be similar to 15 Angstrom. A Monte Carlo simulation of 3-D diffusion in energetically disordered media was applied for analyzing the hole-scavenging behavior. The spatially restricted character of the hole migration was revealed by the simulation. A very slow (up to several tens of milliseconds) recombination of TMPD cations with TCNB anions was also observed, which was explained in terms of a long-range electron tunneling.