Svetlana Jitomirskaya, Yoram Last Power Law Subordinacy and Singular Spectra. II. Line Operators. (318K, postscript) ABSTRACT. We study Hausdorff-dimensional spectral properties of certain ``whole-line'' quasiperiodic discrete Schr\"odinger operators by using the extension of the Gilbert-Pearson subordinacy theory that we previously developed in part I (mp_arc 98-723).