trees figure insertion of into the -tree in figure causes split into two leaves and then split of the parent node when nonleaf node is splitas is the case hereits parent gains child what if the parent already has reached its limit of childrenthen we continue splitting nodes up the tree until either we find parent that does not need to be split or we reach the root if we split the rootthen we have two roots obviouslythis is unacceptablebut we can create new root that has the split roots as its two children this is why the root is granted the special two-child minimum exemption it also is the only way that -tree gains height needless to saysplitting all the way up to the root is an exceptionally rare event this is because tree with four levels indicates that the root has been split three times throughout the entire sequence of insertions (assuming no deletions have occurredin factthe splitting of any nonleaf node is also quite rare there are other ways to handle the overflowing of children one technique is to put child up for adoption should neighbor have room to insert into the -tree in figure for examplewe could make room by moving to the next leaf this technique requires modification of the parentbecause the keys are affected howeverit tends to keep nodes fuller and saves space in the long run we can perform deletion by finding the item that needs to be removed and then removing it the problem is that if the leaf it was in had the minimum number of data itemsthen it is now below the minimum we can rectify this situation by adopting neighboring itemif the neighbor is not itself at its minimum if it isthen we can combine with the neighbor to form full leaf unfortunatelythis means that the parent has lost child if this causes the parent to fall below its minimumthen it follows the same strategy this process could figure -tree after the deletion of from the -tree in figure