Yes, they all have common ancestry. But it would be a long way back, and I'm not sure we know just what the most recent common ancestors are.
All three are multicellular life forms with eukaryotic cells. That is, their cells have nuclei containing their primary chromosomes. The nuclear organization protects those chromosomes from tiny, symbiotic creatures with their own DNA, known as mitochondria, who inhabit the cell and reproduce within it. Eukaryotes are dependent on the mitochondria for some cellular functions.
This symbiosis developed a long time ago, in single-celled life forms--basically, a case of parasites invading cells and developing a symbiotic relationship. Descendants of the single-celled eukaryotes developed into multicellular life forms, including the ones that evolved specialized organs--different sets of cells for different purposes.
The division between plants and animals, of course, separates the ancestry of pine trees from that of whales and mosquitoes. A later separation occurred between the ancestors of vertebrates (such as whales) and those of arthropods (such as insects, like mosquitoes).
Nobody--at least, nobody responsible--suggests that the common ancestry in such cases is at all recent.