  We consider a new idea for a storage model on n nodes, namely stability of
shape. These nodes support K neighborhoods S_i \subset {1, ..., n} and items
arrive at the S_i as independent Poisson streams with rates lambda_i, i=1,
...,K. Upon arrival at S_i an item is stored at node j \in S_i where j is
determined by some policy. Under natural conditions on the lambda_i we exhibit
simple local policies such that the multidimensional process describing the
evolution of the number of items at each node is positive recurrent (stable) in
shape.
