Could be a BLOOD relative, McGoH, but not in the matrilineal line, as mitochondria are passed from mother (only) to children (of all sexes). So you will have your mother's mitochondria, and they are descended from her mother's, and your grandmother's mother's, and so on, back for over half a billion years, since mothers and fathers (i.e. ova being different from spermatozoa) were invented.

You get your Y chromosome from your father, and his father, and so on, the chain is shorter here because back a few tens of millions of years the sex- determination mechanism was different.

The rest of your genes also go back through unbelieveable time, but because of recombination during meiosis they are all mixed up and don't specify which line they came from.