I found this map :
Now it keep me wondering: how would the climate of this world works? keep in mind, I only ask for climate here, about how this world came to be can be ignored.
(I did plan to forset a story in this world, especially regarding its animals, but it can be ignored)
At a glance that much ocean to supply them and no land to stop them means hurricanes would be savage here, and those poor island would suffer a lot when hit by one of them.
In our world when an hurricane forms on warm ocean and gets more energy as it keeps moving on its water, but as soon as it hits land it stops being fed and starts losing energy. Of course this won't apply in this case, as most of the landmasses around the tropics are small and would offer no appreciable obstacle to hurricanes.
Hurricanes reaching as north as UK or North Japan would be common in this world, which would make for pretty interesting late summers, so to say.
I'm not a climate expert, but generally oceans moderate climate. Here is a similar question (thank you @Goodies). Water slows temperature changes, absorbing and releasing vast quantities of heat over time. I would expect a globally more uniform temperature, less seasonal variation, and with lots of thermocline and deep oceans, a bigger buffer against climate change. The thermohaline circulation could be a lot more active on a world with this much water, but without doing some pretty sophisticated modeling I can't say for certain.
I'm guessing the jet streams will be straighter and more stable, and that would contribute to cooler temperatures in the arctic regions. The formation of ice caps would actually accelerate the thermohaline circulation, though, so this could end up going either way for polar temperatures.
The consensus about storms is for increased severity, but I can't find a lot of good references to prove that. Some suggestions (not even remotely hard science) suggest the southern hemisphere has less severe weather and that would indicate all the extra water might help prevent big storms. Others say all that water will provide unrestricted building of bigger and bigger storms. My best guess is that there might be a band of intense storms near the equator, shifting seasonally north or south, with less severe weather in temperate climates.
Water has a lower albedo than most land surfaces & especially ice, so if you were to hold constant the Earth's distance from the sun & axial tilt, etc. then the Earth with only islands would be much warmer.
Water also takes more energy to cool off and warm up as compared to land, so the climate would have less daily, annual and latitudinal variation. Increase in zonal avg. windspeed however would militate in favor of a heightened temperature contrast between the poles & the equator, so whether the latitudinal temperature contrast was increased or decreased would depend on the relative importance of heat transfer via atmospheric vs. oceanic circulation.
With very little land, the Earth may be too warm for even seasonal polar ice. It has been that way in the past after all (Cretaceous, Eocene) and the Earth still had significant exposed landmasses unlike in this scenario.
The Earth would also be warmer due to increased water vapor in the atmosphere from the higher temperatures (as the amount of water vapor in the air is dependent on the temperature). If the Earth became too warm, then at some point the stratosphere would become much more moist (as opposed to the current situation where it is essentially dry), and water from the Earth would be more easily lost to space. In all likelihood, this would eventually lead to the total loss of the world's oceans.
