Cell size varies during the cell cycle and in response to external stimuli. This requires the tight coordination, or “scaling”, of mRNA and protein quantities with the cell volume in order to maintain biomolecules concentrations and cell density. Evidence in cell populations and single cells indicates that scaling relies on the coordination of mRNA transcription rates with cell size. Here we use a combination of single-molecule fluorescence in situ hybridisation (smFISH), time-lapse microscopy and mathematical modelling in single fission yeast cells to uncover the precise molecular mechanisms that control transcription rates scaling with cell size. Linear scaling of mRNA quantities is apparent in single fission yeast cells during a normal cell cycle. Transcription rates of both constitutive and regulated genes scale with cell size without evidence for transcriptional bursting. Modelling and experimental data indicate that scaling relies on the coordination of RNAPII transcription initiation rates with cell size and that RNAPII is a limiting factor. We show using real-time quantitative imaging that size increase is accompanied by a rapid concentration independent recruitment of RNAPII onto chromatin. Finally, we find that in multinucleated cells, scaling is set at the level of single nuclei and not the entire cell, making the nucleus the transcriptional scaling unit. Integrating our observations in a mechanistic model of RNAPII mediated transcription, we propose that scaling of gene expression with cell size is the consequence of competition between genes for limiting RNAPII.