Is it "alright" or "allright"?

Wiktionary marks alright as an "alternative spelling" of all right, and allright as a "common misspelling" thereof. Merriam-Webster only has entries for alright and all right, and this usage discussion:

The one-word spelling alright appeared some 75 years after all right itself had reappeared from a 400-year-long absence. Since the early 20th century some critics have insisted alright is wrong, but it has its defenders and its users. It is less frequent than all right but remains in common use especially in journalistic and business publications. It is quite common in fictional dialogue, and is used occasionally in other writing <the first two years of medical school were alright — Gertrude Stein>.

The stats from the Corpus of Contemporary American English and the British National Corpus look as follows:

            COCA   BNC

all right  59013   6384
alright     1888   8328
allright      36      3

This suggests that alright is much more popular in Britain than in the US. However, the Corpus of Historical American English paints the following picture:

^{X axis: year, Y axis: incidences per million words.}

So, alright seems to be gaining popularity in the States as well.

Lastly, the fact that all right loses one L when written as one word is not peculiar in the least — just think of already, almost, although, albeit, almighty, altogether, and any number of other words formed this way.

The second spelling requires a space: it is either “alright” or “all right”.

The New Oxford American Dictionary says:

Usage: The merging of all and right to form the one-word spelling alright is first recorded toward the end of the 19th century (unlike other similar merged spellings such as altogether and already, which date from much earlier). There is no logical reason for insisting that all right be two words when other single-word forms such as altogether have long been accepted. Nevertheless, although found widely, alright remains nonstandard.

I was taught that "alright" was never correct. I don't see any problem with it in informal contexts, but I would avoid it elsewhere.

I'm my humble and uninformed opinion they are both correct, but are a little different.

I would use "alright" in a sentence such as: "Alright, I finished fixing the engine, now to test it.", or "alright, alright already, I'll fix the brakes." while I would say "The car's running all right, but it really needs a wash."

So, I would use "all right" when it really means all of it's right, while "alright" is used in more informal or derivative uses where it doesn't really mean all is right.

According to Collins Dictionary and Thesaurus (UK, 2nd ed. 2000):

alright is "a variant spelling of all right."
"USAGE NOTE The form alright, though very common, is still considered by many people to be wrong or less acceptable"

The entry for all right includes:
"all-right (US slang) acceptable; reliable."

allright doesn't even merit an entry.

So 'alright' is all right, but 'allright' is wrong, at least in my book.