This paper presents an analysis of the physical properties of craters on asteroid (21) Lutetia, derived from images acquired by OSIRIS, the high-resolution cameras onboard ESA's spacecraft Rosetta. Crater morphology on (21) Lutetia fits very well with the general picture of what was known for previously visited small bodies, with a typical depth to diameter ratio of 0.12. We discuss here the distribution of this parameter all across the surface, but also region by region, and see how it can vary from one location to another and help to distinguish between different geological units. In a later section of the paper we study in more details Beatica region where a deep ejecta blanket filled most of the craters, and estimate the thickness profile of this ejecta based on our analysis of the d/D. We find a good agreement with existing scaling laws, and use this to constrain the scale of the original event that reshaped the surface around the North pole of the asteroid. Finally, we report on the observations of avalanches in several crater flanks, and the presence of many asymmetrical craters with flow-like features, and discuss the evidence for widespread fine material all over the surface. (C) 2012 Elsevier Ltd. All rights reserved.