In this paper, we discuss three physically relevant problems concerning the normal grain growth process.These are: Infinite versus finite size of the system under study (a step towards more realistic modeling); conditions of fine-grained structure formation, with possible applications to thin films and biomembranes, and interesting relations to superplasticity of materials; approach to log-normality, an ubiquitous natural phenomenon, frequently reported in literature. It turns out that all three important points mentioned are possible to be included in a Mulheran--Harding type behavior of evolving grains-containing systems that we have studied previously.

PACS numbers: 05.40.--a, 64.60.--i, 81.10.Jt