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:
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.