The largest liquid fuel engine to have been designed and have components actually tested was the Aerojet M-1.
7.72 meters high x 4.24 m wide (25.3 ft x 13.9 feet) with an ISP(vac) of 428 seconds. It's initial operating capability was for 1,500,000 lbs thrust, with an immediate growth upgrade availability of 1,800,000 lbs of thrust.

An actual part of the M-1 tubomachinery.

For comparison the Saturn-V F-1 engine was 18.5 feet tall x 12.2 feet wide. The increased ISP of the M-1 of 428 seconds to the F-1's 260 and 263 seconds was impressive. Of course it should be when switching from RP-1(USA rocket grade kerosene) to cryo Hydrogen fuels.

There are proposals to use 2 F-1-B engines per booster as a "Advanced Booster" for SLS Block 2(130 tonnes) or 4 F-1's per SLS launch. The F-1B engines are to provide 1,800,000 lbs of thrust per engine, 3.6 million per booster, or 7.2 million pounds of thrust per SLS vehicle. In addition the SLS Block 2 Core Stage will continue to use 4 "new build" RS-25 engines, of which they are currently testing a new pogo-accumulator system that uses new Additive Manufacturing technologies. The new Liquid Boosters could loft 150 tonnes into LEO using 4 RS25 Core Stage Engines. Major work would be required for the mobile Launcher Platforms though. The SLS MLP is already scheduled to be over 1 million pounds overweight, and that's just for the Block 1b SLS vehicle.
Pic showing the POGO accumulator

Since the RS-25 engines of the Core Stage(CS) no longer have to deep throttle like they did on STS(shuttle-down to 67%-72% RPL-rated performance level) during MAx-Q(the area of maximum dynamic pressure on the stack-which for STS was roughly the transonic region) and because the RS25 is no longer in a reusable role, they are expendable now, they will only be asked to throttle down to 80% RPL, but will use a higher 111% for nominal throttling. For STS, the nominal throttling was 104.5% for the Block II SSME, with 111% available ONLY for Contingency Aborts(literally do or die), and 109% for Intact aborts.
15 Main Flight Engines, 2 Development Engines and parts were saved from the Shuttle program, one of the Flight Engines ME-2062 was built in 2010 was never hotfired and ME-2063 was built in 2014. There are now 16 RS-25D(SSMEs which are now referred to as Adaptation Engines as they will fly with all new controllers and of sufficient numbers for 4 SLS missions.
Rain from the 1st test of 2018, in Jan.

2nd Test from 2018 using DE(development engine) DE-0528. Another test using DE-0528 will be done shortly thus completing the Retrofit Engine 1-A test series, then DE-0525 will be installed to commence the Retrofit Engine 1-B test series.(scheduled for 12 hot fires)
E0528 test: 365-second duration, same 'low/high/low' throttle profile between 80% and 111%
http://www.youtube.com/watch?v=8ElM_4ZsH9k?t=001peace
Hog