Dynamics of dust particles of wide ranges of masses and radii in plasmas near material walls was investigated with computer simulations. Both electrostatic sheath and ionizing presheath, which appear near a floating wall, were simulated and stationary plasma parameters distributions were obtained. Dust particles radii and masses are classified with respect to their possible trajectories using numerical solutions of dust momentum and charging equations in the sheath-presheath plasma. We found two critical radiuses that separate dust particles on attached to the wall; incapable to move outside sheath and penetrating deeply in plasma during oscillations around their equilibrium positions. It was shown that for lighter dust particles for which delayed charging significantly effects on theirs dynamics second critical radius does not exist. The critical dust mass which corresponds to that transition was found. Obtained dependencies of the farthest position from the wall which a dust particle can reach in plasma on radiuses for different dust masses showed that the smaller are dust particles the deeper they go to plasma. Scaling of the presheath length can change this penetration depth increases with increasing of the presheath length. The collisionless damping of the dust particles oscillations was observed that conditioned by the effect of delayed dust charging in strong potential gradient of sheath. The possibility to control critical dust parameters with changing of plasma parameters and the wall potential is discussed.