Which preposition: "Write on/at/to this address?"

Solution 1:

You can write on paper or any surface, such as a hand or on a wall.
You can also write on a subject or topic according to this website: http://www.thefreedictionary.com/write+on (but I'm not entirely convinced).

So "Please write on this address" I would interpret to mean the inscriber has to write over a pre-typed address. "On" in this case indicates place. The request sounds odd to me but from a grammatical point of view it is arguably correct.

As for using the preposition "at" I would consider the sentence to be incomplete. A direct object is needed.

"Please write to me/him/her/us/them at this address"

My preferred answer would be: "Please write to this address" You are asked to communicate and transfer your message from one place (presumably your home) to another ("this address"). http://dictionary.reference.com/browse/to?s=t