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DNA methylation is a crucial epigenetic modification that orchestrates chromatin remodelers that suppress transcription, and aberrations in DNA methylation result in a variety of conditions such as cancers and developmental disorders. While it is understood that methylation occurs at CpG-rich DNA regions, it is less understood how distinct methylation profiles are established within various cell types. In this work, we develop a molecular-transport model that depicts the genomic exploration of DNA methyltransferase within a multiscale DNA environment, incorporating biologically relevant factors like methylation rate and CpG density to predict how patterns are established. Our model predicts DNA methylation-state correlation distributions arising from the transport and kinetic properties that are crucial for the establishment of unique methylation profiles. We model the methylation correlation distributions of nine cancerous human cell types to determine how these properties affect the epigenetic profile. Our theory is capable of recapitulating experimental methylation patterns, suggesting the importance of DNA methyltransferase transport in epigenetic regulation. Through this work, we propose a mechanistic description for the establishment of methylation profiles, capturing the key behavioral characteristics of methyltransferase that lead to aberrant methylation.