The Nutanix AHV virtualization guide explains that vGPU-enabled VMs can be live migrated only when the destination host contains compatible GPU hardware and has available vGPU capacity matching the profile assigned to the VM. The documentation states that the VM must have "adequate and equivalent GPU resources on the target host" for migration to proceed. Host affinity is a limiting factor and not a requirement.
Agent VMs are not designed to be migrated. Changing the vGPU profile is not necessary as long as the target host supports the currently assigned profile. Therefore, ensuring the destination host has sufficient compatible resources is the required condition.