92 honda civic with new radiator,hoses top and bottom, water pump, thermostat which later I just removed. When first started the engine cycles up and down the RPM driving it is OK. Big problem I am having is the hose for the overflow from the radiator pops off and the engine overheats. No white smoke from the exhaust. Does not appear to be any water in the oil either. What would cause the amount of pressure to blow off the overflow hose and the engine to overheat. With the exception of the head gasket blown I don't know what else to go for. I don't see any smoke so is the gasket blown or not?

Be sure to properly purge all air from the cooling system. This link may help:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-3.html#post235973

Try installing a new OEM radiator cap--one of the internal valves may be bad.

The new radiator came with a new cap. An added note. This is not my car it is my sons car and I saw that he has the heater core hoses disconnected and the hose just wraps back to the head. It is basically a loop. He did this because he said the core was leaking. The only other things I can think of that was mentioned is a bad valve then? Head rebuild time?

Possibly. Difficult to tell from afar. It sounds like your son, however, has had severe overheating problems, based upon what he has replaced, which could easily have warped the head, damaged the valves, and blown the head gasket. Have him test each cylinder's compression--it will likely shed light on what's wrong.

No water in the oil, no smoke in the exhaust . Yet your saying a blown head gasket?

Engine rpm cycling up and down indicates a possible air leak. That could easily be from a leaking head gasket. If he runs it more, he may soon see water in the oil and white exhaust smoke. Yea, my bet is head damage--there's not much else left that it could be, is there? Think about it--you have completely removed the thermostat and it's still overheating. Was there a severe problem with corrosion or phosphate scale?

Not that I can think of that's why I am here lol. I know I have a good head from a D16A I wonder if that head will work on a d16z6

A simple compression test and/or a leak down test should tell you what you're looking at. Your son has virtually replaced everything except the head. That head is really not the right head for that engine--I would keep it clean and stick with the D16Z6.

Put the correct thermostat in. It needs to be there so as to keep the water in the radiator long enough to cool it.

First of all I would not have replaced it with the wrong thermostat to begin with. Second the thermostat is not used to keep water in the radiator to cool the water. Thermostats are not needed in warm climate states such as Florida . Thermostats will allow a engine to warm up faster which during the winter months is nice however not necessary in the south.

Thermostats are used to raise the engine temperature to the proper temp, not cool the water.

Exactly

My 2002 Dodge Neon would take for ever to warm up. After it did, it would overheat. I replaced the thermostat that was always stuck open(just like if there were no thermostat). Fixed the problem for me. Thank you!