Open center ports P to T, A & B are blocked, in neutral. It is used with fixed gear pump where constant flow must go from P to T ports in neutral. (Technically I think it is tandem center, and open center is really PATB, but open center is the most commonly used term for what you are looking for.
Closed center has PATB all blocked in neutral and is used with variable, pressure compensated pump.
Closed center valve on gear pump = full flow across relief valve pressure at all times when cylinder is not moving = full hp into heat.
Open center valve on pr comp pump = full flow across open center when in neutral, pump runs against its stops at full flow, and if the resulting pressure is low, the pump will trash its slippers.
Almost all splitter projects have fixed gear pumps and need open center valve.