The challenge of designing new tunable nonlinear dielectric materials with tailored properties has at- tracted an increasing amount of interest recently. Herein, we study the effective nonlinear dielectric re- sponse of a stochastic paraelectric-dielectric composite consisting of equilibrium distributions of circular and partially penetrable disks (or parallel, infinitely long, identical, partially penetrable, circular cylinders) of a dielectric phase randomly dispersed in a continuous matrix of a paraelectric phase. The random mi- crostructures were generated using the Metropolis Monte Carlo algorithm. The evaluation of the effec- tive permittivity and tunability were carried out by employing either a Landau thermodynamic model or its Johnson’s approximation to describe the field-dependent permittivity of the paraelectric phase and solving continuum-electrostatics equations using finite element calculations. We reveal that the percola- tion threshold in this composite governs the critical behavior of the effective permittivity and tunability. For microstructures below the percolation threshold, our simulations demonstrate a strong nonlinear be- haviour of the field-dependent effective permittivity and very high tunability that increases as a function of dielectric phase concentration. Above the percolation threshold, the effective permittivity shows the tendency to linearization and the tunability dramatically drops down. The highly reduced permittivity and extraordinarily high tunability are obtained for the composites with dielectric impenetrable disks at high concentrations, in which the triggering of the percolation transition is avoided. The reported results cast light on distinct nonlinear behaviour of 2D and 3D stochastic composites and can guide the design of novel composites with the controlled morphology and tailored permittivity and tunability.