we consider properly immersed two-sided stable minimal hypersurfaces of dimension n. we illustrate the validity of curvature estimates for n \leq 6 (and associated bernstein-type properties with an extrinsic area growth assumption). for n \geq 7 we illustrate sheeting results around "flat points". the proof relies on pde analysis. the results extend respectively the schoen-simon-yau estimates (obtained for n \leq 5) and the schoen-simon sheeting theorem (valid for embeddings).