I have a 2003 Subaru Outback Put new radiator, new hoses, new housing, new tstat, new belts, new Reservoir and hose and flushed it and it still sprays coolant all over the engine from the Reservoir. It doesn't over heat. The temp gauge goes up then when I accelerate it goes down. When it is up, I have no heat or a/c Also put in new relay fuses I'm at a loss, any suggestions?? It has only 138,000 miles
The first thing that comes to my mind is that water pump is not circulating the coolant efficiently, which is causing localised boiling of the coolant and hence the overflowing. Revving the engine may increase circulation sufficiently to improve cooling.
The other thing I thought of is that the coolant reservoir cap is not holding pressure, but presumably you replaced that with the new reservoir.
Before spending any more money on parts (other than a new cap, maybe), I would get a mechanic to check for exhaust gasses in the coolant reservoir to make sure your cylinder head gasket is not leaking.
The easy thing to try is bleeding the system (as a comment suggested) in particular when the cap is off the radiator try to squeeze the upper radiator hose and you should see the level move up at the opening. Sometimes you'll see a bubble and the level will drop a bit. Other parts of the system can also have bubbles (like the cabin heater) after changing the coolant this should mostly work it's way out after running a few minutes.
Assuming you've replaced the radiator cap (which is easiest cheapest and often overcooked) something is causing the pressure to rise over spec,
The water pump was not mentioned, I've changed those on all my Subaru.
Unfortunately if you've had overheating issues before a common issue is the head gasket (especially driver side cyl 1) which may be allowing pressure from your cylinder into the coolant system. other failure modes may affect the engine oil, the good news is that it may be possible to replace these without removing the engine but it is a biggish job.
Re other answer: "coolant reservoir cap is not holding pressure", the coolant reservoir cap isn't supposed to hold pressure. The radiator cap has a spring which allows coolant to flow into the "reservoir" when the system exceeds a certain temp.