RNA polymerase III (Pol III) produces a plethora of small noncoding RNA species involved in diverse cellular processes, from transcription regulation and splicing to RNA stability, translation, and proteostasis. Though Pol III activity is broadly coupled with cellular demands for protein synthesis and growth, a more precise understanding of gene-level dynamics and context-specific expression patterns remains missing, in part due to challenges related to sequencing and mapping Pol III-derived small ncRNAs. Here, we establish a predictive multi-tissue map of human Pol III activity across 19 tissues and 23 primary cancer subtypes by comprehensively profiling the chromatin accessibility of canonical Pol III-transcribed gene classes. Our framework relies on the unique relationship between gene accessibility and Pol III transcription, inferring activity through uniform binary classification of ATAC-seq enrichment at Pol III-transcribed genes. By characterizing multi-context gene uniformity, we provide a definition of the core Pol III transcriptome, broadly active across specialized tissues, and catalog genes with varied levels of context specificity. Our genomic Pol III atlas uncovers variable levels of activity across tissues, including sharp contraction of the Pol III transcriptome in heart and brain tissues and frequent expansion across diverse cancers. We show that both tissue- and tumor-specific genes are significantly enriched within lamina-associated domains (LADs), and that aberrant expression of nuclear lamin proteins is sufficient to induce Pol III-emergent patterns at tumor-specific genes. Together, these findings link Pol III dynamics to subnuclear compartmentalization and provide a resource for better understanding Pol III expansion and small RNA biogenesis in cancer.