Final answer:
RNA polymerase II is responsible for the transcription of mRNA for a globin protein in eukaryotes, as it synthesizes all protein-coding nuclear pre-mRNAs.
Step-by-step explanation:
In eukaryotes, the transcription of mRNA for a globin protein would be carried out by RNA polymerase II. This enzyme is responsible for synthesizing all protein-coding nuclear pre-mRNAs, which includes the globin protein genes. The process of transcription also involves the binding of several transcription factors to complex promoter sequences that facilitate the initiation and regulation of gene transcription. After transcription, eukaryotic pre-mRNAs undergo extensive processing to become mature mRNAs ready for translation.