First, the phrasal verb is indeed take off, which means:
take off (phrasal verb) To leave the ground and begin flight; to ascend into the air
Second, you can use a preposition after a phrasal verb:
The plane took off from the runway.
Third, we need to be careful about omitting the prepositions, because sometimes phrasal verbs can mean different things:
take off (phrasal verb) To remove
So, without a preposition, we could say:
The bulldozer took off the runway, leaving nothing but brown dirt.
Fourth, it is possible to use the same preposition found in the phrasal verb immediately after the phrasal verb; it's not "incorrect." So, if you really wanted to, you could say:
The plane took off off the runway.
However, I'd recommend rewriting that, for a couple reasons:
- Although English doesn't have a rule strictly prohibiting identical consecutive words, they can still be awkward, so it's probably best to avoid them when possible
- Since we know that airplanes normally take off using runways, adding the phrase "off the runway" doesn't really add much useful information
That said, there are other examples I can think of where the last word of a phrasal verb might match the proposition immediately following it:
The hotel was filling up fast, but we checked in in time to get a room.
He came around around twenty minutes ago.
I passed out out by the meadow.
She had no one to root for for the rest of the tournament.
Like I said, though, there are often simple ways to improve such sentences – which is probably one reason you don't run across them very often. For example, you can change the prepositional phrase or the verb:
- The hotel was filling up fast, but we checked in early enough to get a room.
The hotel was filling up fast, but we arrived in time to get a room.
He came around about twenty minutes ago.
He wandered by around twenty minutes ago.
I passed out over near the meadow.
- I fainted out by the meadow.
Or sometimes you can simply rearrange the sentence:
- For the rest of the tournament, she had no one to root for.