Hi OP
The hose part# can found in this thread.
Need some help [Archive] - Club Hummer Offroad

Chris

Thanks!
 

Thanks everyone for the quick replies. The hose is called the crankcase ventilation hose. It is a special order hose. Picked mine up today at the dealership, no one else had the hose. Hose is pretty cheap ($10). Sludge is normal according to the dealership. Like the post before, we just need to clean it out. Dealership indicated that this was caused from the oil spray from the crankcase mixing with condensation in the line. Hope this can help others! I greatly appreciate all your responses and help!
Cheers!

Sludge normal ? Is the removal a scheduled maint item?

If the oil and sludge that collects in the breather hose and intake really bugs you, install one of these: PVC Oil Catch Can Silver : Amazon.com : Automotive

(there are dozens to choose from)

Well would be part of PCV pollution system maintenance.

The oil is normal, the sludge (water in the oil) might be normal in different climates, in our climate here definitely not normal, no humidity and no snow.

The I5 H3 has TWO PCV ports, the one that is apparently baffling you fellows is the secondary, it handles about 30% of the crankcase ventilation that kicks in under heavy throttle. There is a another one (8MM) that vents into the intake manifold which is the primary and handles about 70% under regular driving conditions.

It is not rocket science, rather it is a 1/2" (12MM) hose, any will do, buy a piece at the local auto parts and cut it to length, shape of the hose length is irrelevant.

Heavy throttle will pull in oil vapors, fumes and blow by with very warm air/CO, your intake is cool, the change in temps creates.... condensation. It doesn't matter if you live in a desert, still happens but to a lesser extent. The condensed moisture mixes with the oil residue, and that is what you are left with. Normal if you heavy foot it.

Actually the other one is the clean air supply from the air filter to the crankcase under normal driving.
If there is blowby,the svc lit says,it can backflow up that hose to the air filter, an abnormal condition.
Ive to make up hoses with funny/hard bends,and find it helps to get a long piece and put a loop in it to avoid a kink in the hard bend. As Doc says its just a hose,nothing special,the orfice is where it plugs on to the engine. You might want to see if the hole ,2.5 mm , is plugged while the hose is off.

What does it mean when it's on oil cap and dip stick

That's a sign of a head gasket issue. Sorry to hear that!

Many questions have to be answered first.

Are you losing coolent? Do you only drive short distances, like under 10 miles? Have you made sure your crankcase vent hose is not plugged up?