I will talk about the new construction of genus-zero free boundary minimal surfaces embedded in the unit ball in the Euclidean three-space which are compact and lie arbitrarily close to the boundary unit sphere with 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 talk is based on the joint walk with Professor Nicolaos Kapouleas.