Spanning Pre-disks in a Compression Body

A properly embedded essential planar surface P (not a disk) in a compression body V is called a spanning pre-disk with respect to J,if one boundary component of P is lying in (З)+V and all other boundary components of P are lying in (З)_ V and coplanar with J.In this paper,we show that the number of boundary components of spanning pre-disks in a compression body is unbounded.But the number of a maximal collection of spanning pre-disks is bounded.