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Usually a property is sold with "full title guarantee" due to a standard seller selling with full knowledge of the property.
An auction property is usually sold under "limited title" which means the way it is being sold or the person selling has no knowledge of the property so you cannot ask any questions that you would in a standard purchase that a standard seller would know the answer to.
This is why it is important to thoroughly check the property and have your own searches and inspections carried out.
The Court of Protection Order is just the evidence required to sell the property on behalf of the actual owner.
When you sell you will be selling with full title because you are standard seller and will have knowledge of the property at the time you come to sell.
Splitting the title would still have both full title.
Limited title will not affect getting a mortgage but the valuation would be dependent on the condition of the property. i would being sure you can arrange the funds before putting in an offer at auction.