Earth's primordial ocean was boiled off when Theia impacted the planet and formed the Moon. We don't know how much water that was, or how typical or atypical our situation is. However, it seems strange to assume that a star with sufficient metallicity to form a super-Earth in a habitable zone would lack commiserate ices. I'm sure it happens, but the first guess would be that bigger planet = more primordial water.
Not that that is the entire story. Venus for example, may have had its primordial water blown off during the protostellar phase. So that may be an alternate 'solution' to find a non-Poseidon without a moon.
So the presence of Earth's oceans is determined by several factors.
The first is that our water is water that was trapped inside the planet during accretion, and was slowly driven up over many aeons (there's a paper on this... it was actually calculated with the aid of He3 seepage, which we can safely assume to be primordial when found on Earth, for the most part). This is a volume metric, while the surface area of a planet is naturally an area metric. So bigger planet in habitable zone = deeper oceans.
The second is simply geological activity. While the planet is geologically active, the planet's surface is actually more like a fluid than a solid, if water gets trapped under the surface, it's going to try to boil its way out somehow. Once plate tectonics stops, however, water seeps back beneath the surface of the planet, and just sits there. This is part of why Mars is so dry - lots of water is most assuredly there. A bigger planet, of course, is going to have a more active geology, so the same factor applies.
Planets can also lose water. Occasionally, for innumerable reasons, a water molecule will get sapped, freeing the oxygen of its hydrogen. The smaller the planet, the more likely the hydrogen is to escape. This has had a somewhat meaningful impact on Earth, but the impact on Mars is more drastic. A large enough super-Earth might not ever allow hydrogen to escape in any meaningful quantity, so eventually it re-bonds with free oxygen again.
And then there's simple effects of greater gravity causing larger planets to have smaller features, less water getting tossed off in a giant impact even a-la the moon's formation, or even smaller impacts such as ice comets plowing into the surface.
So taking the above into consideration, even if we're to believe that Earth has more water than average, say, the tendency is going to be bigger planet = more of it covered in water.