Small point, but Ganymede is slightly larger than Titan as moons are measured by their solid surface, though with atmosphere, Titan appears slightly bigger. The drawing is probably accurate, but slightly misleading.
It's worth adding that Titan is out-gassing so it may have, quite some time ago, been larger than Ganymede.
Source
According to wikipedia, the larger, close to Jupiter and Saturn moons are unlikely to have been captured moons.
https://en.wikipedia.org/wiki/Formation_and_evolution_of_the_Solar_System#Moons
Jupiter and Saturn have several large moons, such as Io, Europa,
Ganymede and Titan, which may have originated from discs around each
giant planet in much the same way that the planets formed from the
disc around the Sun.[76] This origin is indicated by the large sizes
of the moons and their proximity to the planet. These attributes are
impossible to achieve via capture, while the gaseous nature of the
primaries also make formation from collision debris unlikely. The
outer moons of the giant planets tend to be small and have eccentric
orbits with arbitrary inclinations. These are the characteristics
expected of captured bodies
and the 3 listed methods of moon formation are:
Co-formation
Impact
Capture.
The largest co-formation ratio is Titan to Saturn, about 1 to 4,000 in terms of mass. Ganymede to Jupiter, less than 1 to 12,000. The wiki article points out that ratios of 100 to 1 are likely giant impacts and you're unlikely to see that kind of ratio in co formation, so a conservative estimate, the largest co-formation you mgiht see might be around a few hundred to 1. If you figure the largest planets are about 12-12.5 Jupiters (more than that, they become brown dwarfs, though a cool brown dwarf orbiting a sun might get called a planet too at greater than 13 Jupiter masses), but lets say, 12 Jupiters. That's about 4,000 earth masses. If we look at a co-formation ratio of a few hundred to perhaps over a thousand to 1 as about the maxiumum, there's a possible ballpark answer of a handul of earth masses might be about as big as a co-formation moon is likely to get in a perfect formation situation, And those would probably be pretty rare.
Giant impacts are different. Pluto-Charon could be an impact generated dwarf planet/moon system and Charon is 1/8th the mass of Pluto. How likely that kind of impact is to happen on a super earth is hard to say, but theoretically a super-earth with a giant impact could have a large moon too - a bigger earth with a bigger impact and bigger moon, but there's problems here. Giant planets are likely to form close to the sun and the orbital sphere of influence gets smaller closer to the sun. Also, giant planets might tend to form thick gaseous atmospheres, retaining all their hydrogen and helium, so too big, it might begin to resemble a gas giant, which aren't as good at creating debris when impacted, so there's a few limiting factors here and we might be limited to, certainly several times larger than our moon, but perhaps not as large as co-formation moons, further from the sun.
Finally, moon capture. While there's no examples of this in our solar system, I see no reason why a large planet couldn't capture another planet, though you then have to determine whether it's a co-planet orbit, which I think a captured planet should be considered, or whether the captured object is a moon. - personally I think a captured planet that orbits a planet would be a co-planet system, so I don't like the capture as a method for getting as large a moon as possible, though I suppose it could be looked at either way.
We know almost nothing about moons in other solar systems (exomoons). The observations are just barely possible with current technology, but very difficult. That's likely going to change in the next few years, but for now we know virtually nothing in other solar systems, so, any present predictions on the largest possible moons would have to be modeled or estimated.
A few articles on exomoons:
http://www.astrobio.net/news-exclusive/new-exomoon-hunting-technique-could-find-solar-system-like-moons/
http://discovermagazine.com/2012/jul-aug/06-hunting-moons-outside-the-solar-system
http://www.space.com/25438-exomoon-around-alien-planet-discovery.html
http://phys.org/news/2014-10-exomoons-abundant-sources-habitability.html
http://blogs.scientificamerican.com/life-unbounded/has-an-exomoon-been-found2/
