something to remember for the future: you also have the option to buy the other half of the co owned player before going to the blind auction. It is the same as buying a full player but you are negotiating just for the 50%.
Unfortunately in FM co ownership is pretty pointless, whereas in real football it is very useful.
Big clubs usually sell half ownership of their younger players so that they are sure the team they are "loaned" at make them play. In regular loans, the team the player is loaned at doesn't care if he sits on the bench all season or not, if he plays well it's all fine, if he doesn't who cares? just let him rot on the bench. while with co ownership it is in their interest to make sure a player gets enough play time and grows in value.
Another reason clubs co own players is because it functions as a sort of "insurance" if the player bought turns out to be ****. Let's say i buy 50% of a striker for 10 millions, if he plays badly i can renew co ownership and see if he gets better, or I send him back, having saved myself another 10 millions which would have been wasted. If he turns out to be good then I buy the other half for a fair price and everyone is happy.
Sometimes teams disagree about the prices, quarrel, and resort to the blind auction, but it doesn't happen that often.
Confusing eh? also broken english doesn't help