Even if the deed to the property is transferred to A & B, or as joint tenants, or any other term, either party may convey it without the joinder of the other. This doesn't make it East half or west half, There is no restriction on A executing a lease without B joining in the lease. Each can deed, mortgage, lease or whatever to his one-half. Again, there is no legal restriction.
Now, suppose, they say they are the sole owner, it doesn't impact the conveyance. It still only conveys one-half.
Depending on certain circumstances, a husband may not deed or lease the property separate from his wife, but if the parties are not married, each can do with their interest as they wish.