The Ort Cloud is 0.03 to 3.2 light-years from the sun [1] and Alpha Centauri is 4.3 light-yeas (per TFA ((that was an nice read)) away and presumably has a similar cloud around it. In what way do these object belong to any star? Could it be that there is a lot more stuff floating around the Milky Way than is commonly acknowledged?

[1] https://en.wikipedia.org/wiki/Oort_cloud