  We investigate a tethered (i.e. fixed connectivity) surface model on
spherical surfaces with many holes by using the canonical Monte Carlo
simulations. Our result in this paper reveals that the model has only a
collapsing transition at finite bending rigidity, where no surface fluctuation
transition can be seen. The first-order collapsing transition separates the
smooth phase from the collapsed phase. Both smooth and collapsed phases are
characterized by Hausdorff dimension H\simeq 2, consequently, the surface
becomes smooth in both phases. The difference between these two phases can be
seen only in the size of surface. This is consistent with the fact that we can
see no surface fluctuation transition at the collapsing transition point. These
two types of transitions are well known to occur at the same transition point
in the conventional surface models defined on the fixed connectivity surfaces
without holes.
