The packing measure of a general subordinator

Precise conditions are obtained for the packing measure of an arbitrary subordinator to be zero, positive and finite, or infinite. It develops that the packing measure problem for a subordinator X(t) is equivalent to the upper local growth problem for Y(t)=min (Y₁(t), Y₂(t)), where Y₁ and Y₂ are independent copies of X. A finite and positive packing measure is possible for subordinators "close to Cauchy"; for such a subordinator there is non-random concave upwards function that exactly describes the upper local growth of Y (although, as is well known, there is no such function for the subordinator X itself).