  The general formalism describing $\vec{A}(\vec{e},e'\vec{p})B$ reactions,
involving polarization of the electron beam, target and ejected proton, is
presented within the framework of the relativistic plane wave impulse
approximation for medium and heavy nuclei. It is shown that the simultaneous
measurement of the target and ejected proton polarization can provide new
information which is not contained in the separate analysis of the
$\vec{A}(\vec{e},e'p)B$ and $A(\vec{e},e'\vec{p})B$ reactions. The polarization
transfer mechanism in which the electron interacts with the initial nucleon
carrying the target polarization, making the proton exit with a fractional
polarization in a different direction, is referred to here as ``skewed
polarization''. The new observables characterizing the process are identified,
and written in terms of polarized response functions and asymmetries which are
of tensor nature. The corresponding half-off-shell single-nucleon responses are
analyzed using different prescriptions for the electromagnetic vertex and for
different kinematics. Numerical predictions are presented for selected
perpendicular and parallel kinematics in the case of $^{39}$K as polarized
target.
