Data Structures, Algorithms, & Applications in Java
Chapter 16, Exercise 51

The operation split(theKey, lessThan, greaterThan) can be done by first doing a get(theKey). If the splay tree has an element with key equal to theKey, then following the get, the element with key theKey is in the root of the splay tree. The left subtree of the splay tree becomes the tree lessThan and the right subtree becomes the tree greaterThan.

When the splay tree has no element with key equal to theKey, then following the get either the root node and its left subtree define the tree lessThan and the right subtree of the root defines greaterThan, or the left subtree of the root defines lessThan and the root together with its right subtree define greaterThan.