  We study within Palatini formalism an f(R)-gravity with f(R)= R + \alpha R^2
interacting with a dilaton and a special kind of nonlinear gauge field system
containing a square-root of the standard Maxwell term, which is known to
produce confinement in flat space-time. Reformulating the model in the physical
Einstein frame we find scalar field effective potential with a flat region
where the confinement dynamics disappears, while in other regions it remains
intact. The effective gauge couplings as well as the induced cosmological
constant become dynamical. In particular, a conventional Maxwell kinetic term
for the gauge field is dynamically generated even if absent in the original
theory. We find few interesting classes of explicit solutions: (i)
asymptotically (anti-)de Sitter black holes of non-standard type with
additional confining vacuum electric potential even for the electrically
neutral ones; (ii) non-standard Reissner-Nordstroem black holes with additional
constant vacuum electric field and having non-flat-spacetime "hedgehog"
asymptotics; (iii) generalized Levi-Civitta-Bertotti-Robinson "tube-like"
space-times.
