1. A computer implemented method of extending virtual memory associated with logical partitions, the computer implemented method comprising: receiving a paging request from an extended virtual memory logical partition on a logically partitioned data processing system, wherein the extended virtual memory logical partition is assigned to physical memory space on the remote computing device, and wherein the paging request comprises instructions for a memory page-in or a memory page-out to the physical memory space assigned to the extended virtual memory logical partition; identifying a location of the physical memory space on the remote computing device assigned to the extended virtual memory logical partition, by a hosting partition located on the logically partitioned data processing system; and sending an extended virtual memory paging request from the hosting partition to an extended virtual memory manager located on the remote computing device using a network connection, wherein the extended virtual memory paging request comprises the instructions for the memory page-in or the memory page-out and the location of the physical memory space on the remote computing device that is being paged-in or paged-out, and wherein the extended virtual memory manager performs a page-in operation or a page-out operation on the physical memory space assigned to the extended virtual memory logical partition in accordance with the instructions for the memory page-in or memory page-out.