Contact phenomena are shown to break the spatial homogeneity of two-dimensional (2D) charged systems almost everywhere between the leads. Various types of contact induced "regular" inhomogeneities in 2D systems are studied. These inhomogeneities are shown to substantially affect different equilibrium and transport characteristics, especially in the Quantum Hall Effect (QHE) regime. Within the framework of the known formalism allowing to determine the properties of separate incompressible (integer) channels in the 2D samples with inhomogeneous density, various local characteristics of typical 2D configurations (Corbino disk and Hall samples) in different extreme cases with respect to the external parameters of the problem (mainly the cyclotron hω_c to contact W energies ratio) are calculated. In the case of hω_c ≥ W the theory deals with a few incompressible strips within the "body" of a 2D system. On the other hand, if hω_c W, a new formalism taking into account the multichannel nature of the problem should be developed. The numerical results obtained are compared with available experiments studying the local characteristics of 2D samples in the QHE regime under the equilibrium conditions.
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