An addition to http://stackoverflow.com/a/42176321/4856258 (using StreamEx)

Test.java

import one.util.streamex.EntryStream;
import one.util.streamex.StreamEx;

import java.util.*;

public class Test {
    static List<List<Integer>> mergeCollections(List<List<Integer>> input) {
        return StreamEx.of(input).foldLeft(Collections.emptyList(),
            (List<List<Integer>> acc, List<Integer> listInner) -> EntryStream
                .of(StreamEx.of(acc).partitioningBy(list -> list.stream().anyMatch(listInner::contains)))
                .mapKeyValue((b, list) -> b ?
                    Collections.singleton(StreamEx.of(list).flatMap(List::stream).append(listInner).distinct().toList())
                    : list)
                .flatMap(Collection::stream)
                .toList());
    }

    public static void main(String[] args) {
        List<List<Integer>> mainList = new ArrayList<List<Integer>>();
        mainList.add(Arrays.asList(0, 1));
        mainList.add(Arrays.asList(0, 1, 2));
        mainList.add(Arrays.asList(1, 2));
        mainList.add(Arrays.asList(3));
        System.out.println(mergeCollections(mainList));

        mainList =  new ArrayList<List<Integer>>();
        mainList.add(Arrays.asList(0,2));
        mainList.add(Arrays.asList(1,4));
        mainList.add(Arrays.asList(0,2,4));
        mainList.add(Arrays.asList(3,4));
        mainList.add(Arrays.asList(1,3,4));
        System.out.println(mergeCollections(mainList));
    }
}