  We construct free boundary minimal surfaces (FBMS) embedded in the unit ball
in the Euclidean three-space which are compact, lie arbitrarily close to the
boundary unit sphere, are of genus zero, and their boundary has an arbitrarily
large number of connected boundary components. The construction is by PDE
gluing methods and the surfaces are desingularizations of unions of many
catenoidal annuli and two flat discs. The union of the boundaries of the
catenoidal annuli and discs is the union of a large finite number of parallel
circles contained in the unit sphere, with each parallel circle contained in
the boundary of exactly two of the catenoidal annuli and discs.
