If you enter an opportunity or an organization into your account it belongs to you. If you decide to share it with another organization you also need to decide if you still want to own it, or if you want to transfer the ownership. To transfer ownership you would select the record, click on "Tools" in the menu bar and select the "Share Records" from the drop down box. Then click on the "Transfer ownership of the selected records" box to select it. This can be a record that you have previously shared but you need to re-share it in order to transfer the ownership. (You may not transfer ownership of "My Organization.") Only the owner can edit or use the opportunity or organization. Everyone else has read only capabilities. You should be aware that transferring ownership of an organization to another account will also transfer ownership of all that organization's opportunities to that account, and will also share all volunteers who are placed and referred with opportunities belonging to that organization.
You cannot own volunteers. It will look like you can transfer their ownership but you do not really own them in the first place. It is set up that way so volunteers can work directly with any agency that shares their records.