The paper has, basically, a methodical character. Dissipative operators are investigated with the aid of the Cayley contraction-transformation on the basis of the "coordinate-free model" of V. L Vasyunin and N. K. Nikol'skii. It is shown that the known forms of the characteristic function and of the selfadjoint dilation can be obtained as various realization of a general scheme. One obtains also new formulas for the dilation and its eigenfunctions, generalizing B. S. Pavlov's formulas for the Schrödinger operator on the semiaxis with a real potential and complex boundary condition. Examples are considered.