We study the long time evolution of a large data structure while inserting new items. It is implemented using a well known computer science approach based on 2-3 trees. We have seen self-organized critical behavior on this data structure. To tackle this problem we have introduced and studied experimentally three statistical magnitudes: the stress of a tree, the sequence of jump points and the distribution of subtrees inside a tree. The stress measures the amount of free space inside the 2-3 tree. When the stress increases some part of the tree is restructured in a way close to an avalanche. Experimentally we obtain a potential law for stress distribution. When the tree does not have more free space in any internal node, needs to grow up. When this happens, the height of the whole tree increases by one and we have a jump point. Experimentally these points have good expected behavior.A 2-3 tree is composed from a great number of other 2-3 trees called their subtrees. We have studied experimentally the distribution of the different subtrees inside the tree. Finally we analyze these results using simple theoretical models based on fringe analysis, Markov and branching processes. These models give us a quite good description of the long term process.