Alongside (an adverb and a preposition) is in present-day English a single word, although OED has the etymological note "[properly a phrase, ALONG prep. + SIDE.]". It is hard to find the theoretically possible writings with two ('along side'). Writing the sound as three separate words, however, as part of geographical or geometrical descriptions, is not uncommon: "Its shape is roughly that of a very broad triangle, with two short borders and a long side facing the sea."
Alongside is in origin a nautical term, and is still used literally in the context of ships and shipping..
- As an adverb, it means 'along [i.e. beside or parallel to or close to] the side of [a ship or structure]'. So the commander of a ship may invite a small boat to 'come alongside', order a captive vessel to 'lay itself alongside'.
- As a preposition, alongside is used with a prepositional complement, a noun or pronoun: "our vessel lay alongside[prep.] (our defeated enemy)(prep. compl.}". The construction with a single word preposition ('alongside' + prepositional complement) runs together with a construction with a compound preposition alongside[advb] + of[prep] + (prep. complement): "Come alongside of me" is as acceptable as "Come alongside me", and even "Come alongside".
- Figuratively, alongside has a much less clear meaning. It is used by many modern writers (in more than the "financial pages" noted by Burchfield's Fowler) as a general connective: 'as well as', 'together with', 'in addition to' or even 'and'. The sense in which it is best used is one in which the items being linked are to be seen as of similar type, and to be supporting each other: "The proprietor bought an evening paper to run alongside of his stable of dailies."
Both the preposition and the adverb should nevertheless always be written as one single word nowadays.