1. An apparatus for replacing a failing physical processor, the apparatus supporting multiple logical partitions, the logical partitions including dedicated partitions and shared processor partitions, the dedicated partitions supported by virtual processors having assigned physical computer processors, the shared processor partitions supported by pools of virtual processors, the pools having assigned physical computer processors, a computer memory operatively coupled to the physical computer processors, the computer memory having disposed within it computer program instructions capable of: assigning priorities to the dedicated partitions and to the pools of virtual processors: detecting a checkstop of a failing processor: retrieving the failing physical processor's state; replacing by a hypervisor the failing physical processor with a replacement physical processor assigned to a dedicated partition or pool, which dedicated partition or pool has the lowest priority among the priorities of the dedicated partitions and pools, wherein the dedicated partition or pool having the lowest priority is a dedicated partition, and replacing the failing physical processor includes terminating the dedicated partition having the lowest priority; and assigning the retrieved state of the failing physical processor as the state of the replacement physical processor.