A coarse-grained model of branched polymers confined in a slit formed by two parallel impenetrable surfaces that were attractive for polymer segments was developed and studied. The model chains were regular stars consisting of f=3 branches of equal length. The positions of chains were restricted to vertices of a simple cubic lattice. The chains were at good solvent conditions-the excluded volume was the only interaction between the segments of the chain. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local changes of conformation. The dependence of chain mobility on the width of the slit and the polymer concentration was studied. The conditions at which the strongly adsorbed chains could swap between both confining surfaces were studied. The mechanism of the chain motion was also discussed.