1. A computer-implemented method of dynamically controlling memory affinity of a shared memory logical partition, the method comprising: determining at least one home node assignment for a logical partition of a plurality of logical partitions in a data processing system, the plurality of logical partitions of the data processing system sharing availability of a defined amount of memory in a shared pool of physical memory absent concurrent access to any physical page of the physical memory, the logical partition running on a plurality of nodes of the data processing system, with each assigned home node being one node of the plurality of nodes and at least one home node comprising a plurality of physical processors of the data processing system; determining a desired physical page level per node for the logical partition; and allowing the logical partition to run and using the at least one home node assignment and the desired physical page levels for the plurality of nodes in the dispatching of tasks to physical processors in the plurality of nodes and in hypervisor page memory management to dynamically control memory affinity of the logical partition in the data processing system; and