Diagrams and descriptions of the F1 engine as used on the Saturn V booster identify a turbine exhaust manifold which leads down from the fuel turbopump and wraps around the main nozzle. As it winds around the nozzle it gets progressively smaller in diameter. This feature can be seen in images and models of the engine. What exactly is the path of the turbine exhaust - where/how does it discharge from the manifold? Does it enter the nozzle to join the main thrust exhaust? Why was it designed as it was?
The F-1 exhaust consists of 2 parts: the nozzle and the nozzle extension. The manifold sits at the point where they meet.
The exhaust gases from the turbine are fed through the manifold into the nozzle extension. The passage was designed to guide this gas along the wall of the nozzle extension. This gas was cooler than the main rocket exhaust gas, so this design reduced the thermal load on the nozzle extension.
From the NASA fact sheet (page 3):
The interior of the nozzle extension is protected from the engine exhaust gas environment (5800 F) by film cooling, using the turbine exhaust gases (1200 F) as the coolant. The gases enter the extension between a continuous outer wall and a shingled inner wall, pass out through injection slots between the shingles, and flow over the surfaces of the shingles forming a boundary layer between the inner wall of the nozzle extension and the hotter exhaust gases exiting from the main engine combustion chamber.
Here's a cross-section of the manifold (borrowed from Herorelics.org):
And another view:
The nozzle is cooled by fuel: the fuel is fed through channels in the nozzle wall. The channels end at the top of the nozzle, where the fuel is fed though the injector plate to be burned. Here's a diagram: