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Since about 1990 astronomers been able to detect planets around other stars, using a couple different techniques, which is amazing.

By this point, do we know whether planets form only around single systems, only around multiple systems, or both??

(Surprisingly you can't find this general issue explained in popular writing. I think it's "obvious background knowledge" to experts, hence just doesn't get outlined explicitly in popular writing.)

So, as of mid 2016:

(i) About how many exoplanets do we know of (say, with good certainty),

(ii) In fact, how many (if any) of these are around single-star systems?

(iii) How many (if any) are around multiple-star systems?

If indeed it is possible to have planets in multiple systems: is it just a planet going around one of the stars, or is "all the way around both" known?

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    $\begingroup$ There appears to be minimal prior research going on here. There are many planets known in multiple star systems - of both types (circumbinary and orbiting one star). $\endgroup$
    – ProfRob
    Commented Jul 13, 2016 at 5:54
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    $\begingroup$ Two more examples on arXiv just this morning, arxiv.org/abs/1607.03038 arxiv.org/abs/1607.02525 $\endgroup$
    – ProfRob
    Commented Jul 13, 2016 at 12:52
  • $\begingroup$ @Lelouch Circumbinary planets have to be at least ~5 times further way than the binary separation. There also appears to be a lack of planets around binaries with periods <7 days. This adds up to circumbinary planets must have periods >35 days. These are harder to find both in transit and doppler surveys. $\endgroup$
    – ProfRob
    Commented Jul 13, 2016 at 12:55
  • $\begingroup$ @JoeBlow Actually, I was wrong. The second paper seems to detail the planet I linked to. The first is actually new, and it is not clear from the abstract whether a planet has been spotted yet. $\endgroup$
    – called2voyage ♦
    Commented Jul 13, 2016 at 14:34
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    $\begingroup$ @FJC I don't think Rob meant that he expected users to search arXiv. If you google "circumbinary planets" a list comes up immediately. I think that is what Rob was talking about. The OP earlier stated that he was already familiar with the term "circumbinary planet", but in his post he is wondering if any have even been discovered. Rob, I think, is wondering why the OP didn't check google first, or if he did why he didn't include an explanation of why the search results were unsatisfactory. $\endgroup$
    – called2voyage ♦
    Commented Jul 13, 2016 at 16:22

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There are currently 3424 planets identified (including those in the Solar System and unconfirmed exoplanets). Of these, 3310 are confirmed exoplanets.

Out of the 3424, 180 are in binary (or multiple) star systems. Of those, 28 are circumbinary. I am not certain if any circumternary planets have been identified, though I know some circumternary disks have.

It is more difficult to identify circum-n-ary planets than those that only revolve around one star, so these numbers might not precisely represent the actual proportions.

Source:

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  • $\begingroup$ this answer is absolutely amazing, thanks. my grasp of the outline of the galaxy has been increased spectacularly. I wish I could send over money :) $\endgroup$
    – Fattie
    Commented Jul 13, 2016 at 16:32
  • $\begingroup$ @JoeBlow No need for compensation, a better answer would give you some theory about the likelihood of formation of circum-n-ary planets. Mine is just counting rows from a spreadsheet. $\endgroup$
    – called2voyage ♦
    Commented Jul 13, 2016 at 16:33
  • $\begingroup$ just for the sake of being anal. 3310 confirmed. regarding the 180 and 28 figures: are those two numbers "confirmed" category or "identified" category? thanks! $\endgroup$
    – Fattie
    Commented Jul 13, 2016 at 17:44
  • $\begingroup$ @JoeBlow As I specified, those are from the 3424 which includes confirmed and unconfirmed. Unfortunately, the list I was looking at didn't have a column indicating which were confirmed. $\endgroup$
    – called2voyage ♦
    Commented Jul 13, 2016 at 17:45
  • $\begingroup$ exoplanets.org is more authoritative and discriminating in my view. $\endgroup$
    – ProfRob
    Commented Jul 14, 2016 at 0:36

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