The properties of simplified lattice models of confined branched polymers were studied by the Monte Carlo method. Model chains were located between two parallel impenetrable surfaces. The distance between surfaces, as well as the chain length, were varied. The model chains consisted of f = 3 branches of equal length (star-branched polymers) and were based on a simple cubic lattice. The model was athermal and the excluded volume was introduced. Monte Carlo sampling algorithm using local chain micromodifications was applied. Both static and dynamic properties of the system were investigated. The differences between star-branched chains and linear ones which were trapped between walls were discussed. The behavior of static properties made it possible to construct a universal curve presenting the effect of surface-to-surface distance on chain dimensions, The possible explanation of the shape of this curve was given. The changes of dynamic properties were discussed in the context of possible chain's mechanism of motion.