1. A method comprising: generating, via at least one computer system, a logical tree in which each node in the logical tree represents a corresponding one of multiple computers in a cluster having controlled access to a storage resource, the logical tree including: i) a root node representing a corresponding root computer in the cluster having exclusive access to the storage resource; ii) a first tier of nodes beneath the root node, each node in the first tier having a corresponding pointer to the corresponding root computer of the logical tree; and iii) a second tier of nodes beneath the first tier, each node in the second tier having a corresponding pointer to a node in the first tier; receiving a request for access to the storage resource; and utilizing a set of pointers at multiple tiers in the logical tree to forward the request up the logical tree through at least a portion of the multiple computers in the cluster to the corresponding root computer of the logical tree; wherein utilizing the set of pointers in the logical tree to forward the request to the corresponding root computer includes: retrieving a first pointer from the logical tree, the first pointer being associated with a first computer in the cluster, the first computer in the cluster generating the request for access to the storage resource, the first pointer specifying a second computer in the cluster; and utilizing the first pointer to forward the request from the first computer to the second computer; receiving the request at the second computer; retrieving a second pointer from a rendition of the logical tree, the second pointer being associated with the second computer in the cluster, the second pointer pointing to the corresponding root computer in the cluster; and forwarding the request from the second computer to the corresponding root computer; the method further comprising: executing a transfer of access rights to the storage resource from the corresponding root computer to the first computer making the request; in response to facilitating the transfer of access rights from the corresponding root computer to the first computer, modifying the logical tree so that the first computer becomes the new root computer in the logical tree; and updating pointer values associated with at least a portion of computers other than the first computer in the cluster such that the updated pointer values point in a direction up the logical tree towards the first computer.