1. A computer system supporting virtual desktops on server computers for access by remote user computers, comprising: a plurality of server computers interconnected on a service provider computer network; each server computer comprising computing resources, including at least processing units and memory, configured to support a plurality of virtual desktops utilizing the computing resources; for each of a plurality of enterprises, a plurality of desktop managers for the enterprise the plurality of desktop managers including for a first enterprise: a first desktop manager assigned to the first enterprise, wherein one or more server computers are assigned to the first desktop manager, wherein the assigned one or more server computers are specifically configured to support virtual desktops provisioned according to hardware resource requirements specified by a first desktop model, and wherein the first desktop manager comprises computing resources configured to manage virtual desktops according to the first desktop model; and a second desktop manager assigned to the first enterprise, wherein the second desktop manager is associated with one or more server computers assigned to the second desktop manager and that are configured to support virtual desktops according to resource requirements of a second desktop model distinct from the first desktop model, and wherein the second desktop manager comprises computing resources configured to manage virtual desktops according to the second desktop model; wherein in response to a request from the first enterprise to provision virtual desktops for a first pool of users, the request specifying the first desktop model, a resource manager selects the first desktop manager to manage virtual desktops for the first pool of users based on the specified desktop model and the available resources of the server computers managed by the first desktop manager, and wherein in response to a request from the first enterprise to provision virtual desktops for a second pool of users, the request specifying the second desktop model, the resource manager selects the second desktop manager to manage virtual desktops for the second pool of users based on the specified desktop model and the available resources of the server computers managed by the first desktop manager.