During cell division, DNA becomes equally distributed between the daughter cells. But how is RNA content distributed in the daughter cells?
RNA is either swimming in the cytosol or be associated with the ER (endoplasmatic reticule) during co-translational protein import into the ER (see secretory pathway).
So in order to answer your question: Daughter cells inherit their RNA simply by chance as cytokinesis just cuts the mother in half and each RNA finds itself on either side, OR they are separated just like the ER.
Each cell 'should' have the same copy number of each RNA, but since daughter cells simply produce RNA all the time, there is no need to be as precise as with chromosomes.
However, there are some specialized motor protein complexes that transport specific RNAs to one (like myo4d transporting RNA along actin filaments). This is called 'asymmetric division'. Please start your research here.