Transcription

Basically I'm stuck. mRNA is single-stranded and therefore able to pass through the nuclear pores. But in my textbook, it goes through the process of transcription (breaking of hydrogen bonds, two separate strands, free RNA nucleotides forming H bonds with template strand) which ends up with a double stranded molecule. Then it says mRNA moves out of pores, and attaches to a ribosome. But does the molecules split up again after so it's single-stranded?