  The cascaded production and dynamics of electron-positron plasma in
ultimately focused laser fields of extreme intensity are studied by 3D
particle-in-cell simulations with the account for the relevant processes of
quantum electrodynamics (QED). We show that, if the laser facility provides a
total power above 20 PW, it is possible to trigger not only a QED cascade but
also pinching in the produced electron-positron plasma. The plasma
self-compression in this case leads to an abrupt rise of the peak density and
magnetic (electric) field up to at least $10^{28}$ cm$^{-3}$ and 1/20 (1/40) of
the Schwinger field, respectively. Determining the actual limits and physics of
this process might require quantum treatment beyond the used standard
semiclassical approach. The proposed setup can thus provide extreme conditions
for probing and exploring fundamental physics of the matter and vacuum.
