This is a 6.0-star Fillomino Connection puzzle.
Unless I’m missing something that makes this puzzle trivial, this puzzle is the hardest puzzle I ever constructed, thus the 6.0-star rating. (It was 7.0-star, but I realized it’s not that hard.) Moreover, it’s an almost-perfect 4-rotational symmetry (just because of the givens; but anyway, if the givens are also symmetric, the puzzle difficulty takes a fall). I think I misjudged this puzzle’s difficulty; comment or e-mail me if you think so.
On an unrelated note, please see the comments of Puzzle 038 and decide whether I should move this to my website with this blog becomes simple notices about the puzzles or keep this as a blog.