I did a lot of research into this topic when I was designing the system for our lithium conversion on our '21 R27OB. Part of that was installing a logging shunt between the Yamaha F300 and the starting battery so I could see exactly how much current and voltage was being put out by the motor. This data will not be the same as you would see when monitoring a typical battery shunt that is measuring current going into a house battery because the engine, start battery and house loads are consuming power that is not entering the house battery. My configuration is engine>start battery>ACR>thruster battery>Victron Orion XS 50A>house battery.
A quick note: In grossly simplified terms, an engine generates electricity by moving a magnet (rotor) past a coil of wire (stator). The F300 does not really have an "alternator" like we think of in a car or an inboard engine. It has parts and pieces that are similar, but it is a pretty antiquated system that is closer to the electrical system in your gas lawnmower. A actual alternator can vary the magnetic pull of the magnet to increase or decrease the output. Like watson1987 pointed out, when you ask an alternator to work at full output for an extended period, bad things can happen.
The Yamaha outboard on our boats are "permanent magnet alternators", meaning there are just regular magnets stuck on the underside of the flywheel. There is no capability to vary the magnetic pull, it is what it is. When the magnet whizzes past the coil of wire, a current is generated. Generally, faster whizzing means more current, up to a point. So at any given speed, the "alternator" is "giving it all she's got", all the time. Any excess current that's not used by the boat is shunted to ground and wasted as heat, which is why the electronics of the charging system are water cooled. If our engines are run properly, in good condition, with good water circulation, they should be able to deliver their rated output continuously. If there is a time-limit factor, I haven't reached it yet.
The most I've seen coming out of our F300 to the start battery is 60 amps. Normally, it's somewhere around 50-55 amps if there is enough power demand. Like Mike said, we usually see amperage in the 40's going into the house battery. The longest I can recall running the charging system at full-tilt is somewhere over 2 hours at 4800 rpm. That was with the water heater on so we were still using more power than the F300 was producing. One thing I've seen is that over time, the voltage can start to decrease while the current remains at around 50A. I'm assuming this is the electronics de-rating because of the heat factor, but I haven't measured it yet. So although the current output is at 50A, you get less power (aka "work") at 13 volts than you do at 14 volts.
FYI -I'm not a Yamaha tech or alternator expert, this is just my experience.