You are correct, of course, in that "a lot" is two separate words. But, most people aren't aware that this is NOT formal English (at least not when meaning "much" or "many"). When writing a business letter, formal paper, etc., "a lot" is not acceptable. Ex. "I have a lot of experience teaching children." On a resumé or in a job application, this is incorrect. It should be something like the following: "I have 10 years of experience teaching children." "I have extensive experience teaching children."

I never write 'alot'. why? I don't know. And I noticed Erik's answer is helpful. Thanks.

yes.

yes, luckily, I'm aware of that. maybe, the word 'a lot' sounds the same with 'allot' (to distribute as in small portion) that makes someone mistakenly write it. thanks anyway for this. :)