As in, a certain amount of space dust is ice (thus, arriving continuously) or just in the form of comets that strike once in a zillion years?
In a book Impact Earth: Asteroids, Comets and Meteoroids: The Growing Threat by Austen Atkinson, I seem to remember reading that we get a regular rain of ice here on earth from comet dust and space debris. Unfortunately, the book does not have a very good Index so I couldn’t find the info. on how many tons a year are added to our water supply.