Thin films of cyanobiphenyl liquid crystals (nCB) deposited on water or glycerol have been studied in the nematic temperature range. A common property of the systems is the hybrid anchoring conditions at the film interfaces. The preferred orientation of the nematic director is planar at the liquid interface, and it is homeotropic and somewhat weaker at the air interface. The resulting structure of the film depends on its thickness. Films thicker than 0.5 mu m show the usual defects of nematics. Between 0.5 mu m and 20-30 nm, complex instability patterns such as stripes, "chevrons", or squares are observed in extended films. Then there is a forbidden range of thickness below in which much thinner structures (usually monolayers and trilayers) are present. The present paper investigates this common behavior in various systems and gives arguments for its analysis.