A friend and I kinda worked through this once. You have floating plants and kelp forming clumps, basically the plants are a series of gas-bags with leaves and root. there are already floating plants but for the ocean you will need greater buoyancy hence the gasbags. picture the sargasso sea on steroids.
other types of plants colonize these mats adding larger plants, more gas bags, deeper roots. the roots start to collect debris and will house lots of animals, the roots of some plants may even be designed to tangle and hold animals for supplemental nutrients.you might have filter feeding animals also colonizign them and each dead plant is going to add more "soil" to the islands. eventually as the mats get large enough they begin to support mangrove like trees with light balsa like wood and maybe their own wood floats or coconut like growths.there trees would favor being wide and spread out instead of tall for stability. the more animals and plants colonize the mats the more debris is added when they die encouraging bigger plants. insects, crabs, maybe amphibians, and millions of fish would colonize such things.
the plants are held together by intertwining rooks and tendrils, and "islands" may be torn apart during storms if they get too big, and would occasionally sink. they would naturally be pushed towards the ocean gyri so soon you would have many "islands" close together or even joining.
on a water world these might very well have evolved from sargassum kelp. Humans would need to build platforms to live on, but would have to be careful cover too much and too many plants might die causing the whole thing to sink.
trees might drop floating twisty nuts that get tangled in in mats where they sprout after several years, giving the mats time to build up around them. the trees roots would spread wide to help hold the mat together and to get their nuts to the edge where they need to be.