The standard splitter hydraulic circuit has a suction line from the bottom of the tank, often one size larger than the rest of the lines, going to the pump intake. It is VERY important that you not add any obstructions or restrictions to this line, as doing so can cause the pump to cavitate as it pulls a vacuum, and rapidly self destruct.
From the pump there will be a high pressure line to the valve - if you put a guage on the system, this is where it should be. Note that while this line is billed as high pressure, the actual pressure on it will vary with the splitter load, and will actually only get "high" while you are splitting. However this line MUST be made with a high pressure hose, and all fittings on it should be high pressure rated hydraulic fittings - DO NOT use "schedule 40" plumbing parts, they will not take the pressure.
From the valve you will have a high pressure line going to each side of the cylinder, and a low pressure line going back to the tank. You should put a good hydraulic fluid filter in this return line.
When the valve is in the neutral the pump will circulate oil from the tank, through the valve and back to the tank.
When the valve is in either the extend or retract positions, it will send the fluid from the pump through the high pressure cylinder line to ONE side of the cylinder causing it to move. The moving piston will push the fluid out of the other side of the cylinder into the return line, and back to the tank.
If you hit a gnarly round, or run the cylinder to it's travel limit, the pressure in the high pressure lines, valve, etc. will build until the pop-off relief valve in the operating valve opens and diverts the excess flow into the return line back to the tank - note that this will cause the fluid to heat rapidly, and is generally hard on the equipment, it is best avoided as much as possible.
I would totally agree with the other posters on disconnecting the belt from the pump when not using it for splitting (or other hydraulic applications) but I would go even further and say that it would be best if you can keep the pump attached to the splitter parts and avoid the quick disconnects. Even the best QD fittings add a certain amount of flow restriction, and while this is tolerable on the high pressure and return lines (not ideal, but OK, best to go up at least one size on the QD fittings, though that gets expensive) IMHO it's problematic at best on the suction line. If you did have to leave the pump on the tractor, I'd keep the tank on it as well, even though it's a good bit of extra weight) so that the suction line would be unrestricted. I'd put the same size, matching QD fittings on the pressure and return lines so that when I detached the splitter, I could plug the two lines back into each other, both to keep the crap out and make sure that if the pump does turn at all, at least the fluid will be able to circulate.
Gooserider