Step 1: Trace the renal tubular pathway to its endpoint. Filtrate passes through the proximal tubule, loop of Henle, distal tubule and collecting ducts, finally reaching the largest terminal ducts in the renal medulla.
Step 2: These terminal papillary ducts are the ducts of Bellini. They are the widest collecting channels and sit at the tip of the renal pyramid.
Step 3: They discharge urine through the sieve-like $area\ cribrosa$ on the renal papilla into a minor calyx, confirming a purely renal location. The pancreas, liver and salivary glands have their own named ducts and none carry this eponym.
Step 4: The organ that contains the ducts of Bellini is the kidney.\[\boxed{Kidney}\]