The statistical properties of the passive scalar near walls in random flows assuming a weakness of its diffusion have been investigated. Then, at advanced stages of the passive scalar mixing, its unmixed residue is concentrated in a narrow diffusive layer near the wall. The numerical simulations have revealed the structures responsible for the passive scalar transport to the bulk; these are passive scalar tongues pulled from the diffusive boundary layer. The passive scalar integrated along the wall possesses a well-pronounced scaling behavior. An analytical scheme, giving exponents of the integral passive scalar moments has been proposed. The exponents reasonably agree with the calculations in 3 d.