  The free energy cost of confining a star polymer where $f$ flexible polymer
chains containing $N$ monomeric units are tethered to a central unit in a slit
with two parallel repulsive walls a distance $D$ apart is considered, for good
solvent conditions. Also the parallel and perpendicular components of the
gyration radius of the star polymer, and the monomer density profile across the
slit are obtained. Theoretical descriptions via Flory theory and scaling
treatments are outlined, and compared to numerical self-consistent field
calculations (applying the Scheutjens-Fleer lattice theory) and to Molecular
Dynamics results for a bead-spring model. It is shown that Flory theory and
self-consistent field (SCF) theory yield the correct scaling of the parallel
linear dimension of the star with $N$, $f$ and $D$, but cannot be used for
estimating the free energy cost reliably. We demonstrate that the same problem
occurs already for the confinement of chains in cylindrical tubes. We also
briefly discuss the problem of a free or grafted star polymer interacting with
a single wall, and show that the dependence of confining force on the
functionality of the star is different for a star confined in a nanoslit and a
star interacting with a single wall, which is due to the absence of a symmetry
plane in the latter case.
