  In the present paper, the 3+1 decomposition of the spacetime onto
hypersurface(s) is analysed and established for theories within the Palatini
formalism by considering a general function of the Ricci scalar in the
gravitational action. The corresponding Gauss-Codazzi relations are obtained
and the boundary term that has to be subtracted in the gravitational action is
easily deduced. Then, these relations are applied to the so-called ADM
decomposition to describe the foliation of the spacetime onto hypersurfaces of
constant time within these theories. Finally, the junction conditions are also
obtained by using a decomposition in Gaussian normal coordinates, which
coincide with the conditions deduced previously through different approaches.
