To designate a new owner for the space, you must leave the space you own. As part of the leaving process, you will be able to select the new owner.
To leave a space, click the Spaces header in the left sidebar and hover over the space name until you see an arrow next to it. Select "Edit space" to access the Edit Space window. Then click "Leave space" at the bottom of the window.
A confirmation popup window will appear. Choose the new owner for this space and then select “Leave”. You will leave the space and all items assigned to you will be reassigned as described in this knowledge base article: http://support.kona.com/entries/21859602-what-happens-to-tasks-i-m-on-when-i-leave-a-space.
Note: If you wish to change ownership of the space but remain in the space, have the new owner invite you back into the space. After re-joining the space, you will be a regular team member.