We present a Monte Carlo study of molecular ordering in nematics with dispersed regular and random arrays of straight and distorted polymer fibrils. We focus on the collective molecular reorientation -the switching -resulting from the competing aligning effects of fibrils and of a progressively applied transversal electric field, and identify stuctural Fréedericksz and saturation transitions. The role of fiber topography in the switching behavior is monitored by simulating electric capacitance: slightly distorted fibrils are shown to give a sharper switching. PACS number(s): 61.30. Cz, 61.30.Gd While simple nematic liquid crystals (LC) are now well understood, nano and mesoscale composites where LC interact with random or regular perturbers [1-3] offer fascinating examples of complex systems, challenging both from the technological and fundamental point of view. Such perturbers consist, e.g., of thin (even nanometric) polymer fibers obtained by polymerization of monomers dissolved in LC that can either memorize the order of the host LC phase [3], or follow a regular pattern as defined in a lithographic formation process [4]. The fiber topography depends sensitively on the polymerization conditions, such as temperature, curing light wavelength and intensity, or monomer solubility [5]. Because of their high surface-to-volume ratio the polymer fibrils influence orientational ordering of the surrounding liquid crystal even at low polymer concentrations [3,[6][7][8]. The actual ordering is affected by the competition between effects of the fiber network (anchoring), temperature, and external fields. Apart from exhibiting a variety of interesting confinement-related phenomena, such composite materials are promising also for the construction of electrooptical devices, based on the "switching" phenomenon. This consists of a reorganization of the nematic director -initially aligned by the polymer network -by applying an external electric field producing changes in electric capacitance, optical transmission, light scattering, etc [3,[6][7][8]. Thus studies of formation and properties of liquid crystaldispersed network systems (LCDNS) are very timely, also for the next generation of LC displays [4,6]. In the past there have been several studies devoted to LCDNS, both experimental and theoretical [6][7][8], but so far the effect of such complex confinement was described only phenomenologically in terms of an effective field [6], while there have been virtually no investigations at the microscopic level [9]. In this Letter we investigate the field-induced changes of molecular ordering in LCDNS by means of Monte Carlo (MC) simulations, starting from a simple pairwise potential and giving great emphasis to the role of polymer network topography.Our simulations are based on the Lebwohl-Lasher (LL) model [10] in which uniaxial nematic molecules (or closepacked clusters containing up to 10 2 molecules [11]) are represented by unit vectors ("particles") u i . The LL model, despite having particles fixed onto sites of a cubic la...