I need the largest hose that goes into the coolant reservoir. It's the one that has a factory T split permanently clamped onto it, and the other end appears to go into the upper intake.
What exactly is that hose called?

 

2003 Jaguar X-Type Parts - Jaguar Parts Center - Call (800) 510-1401 for Genuine Jaguar Parts and Accessories

Cooling system diagram and part numbers.

 

Just bought that one myself. URO part #C2S23485. Found at rockauto for $13. Also on Amazon. Molded t-fitting with metal nipple. No plastic. See pic.

 

I needed to replace 3-way hose for Ford Expedition. I bought plastic 3-way connector from NAPA, 3 clamps and 3' hose. Problem solved.