Usually disk packing problems require that no two disks of the packing intersect.
Does anybody know if the problem has been studied when disks may intersect but they are not allowed to contain the center of any other disk?
Usually disk packing problems require that no two disks of the packing intersect. Does anybody know if the problem has been studied when disks may intersect but they are not allowed to contain the center of any other disk? 


Yes. Here is an example: Rigidity of infinite disk patterns by ZhengXu He. 


There is a subject called "circle packing". There are many exciting results, including the one mentioned in the previous answer. The subject originates from a Thurston conference talk. The discs bounded by circles are sometimes allowed to intersect. See, for example the book of Ken Stephenson, Introduction to circle packing, MR2131318. 

