Publishing income is an important and valuable source of income. This includes mechanical license fees, public performance rights (e.g. payments you get from ASCAP, SESAC or BMI when your song is played on the radio or in a store or restaurant), synchronization rights (when your song is used in a movie or on TV) and more. Fees for these rights are paid only to the copyright holder of a song. If you wrote the song, you own the copyright in the song unless you transfer that ownership to another person or company.
As you have seen from the previous FAQs, income from royalties can not be counted on. Often (beyond the initial advance) the only monies a musician can really count on receiving down the line are the publishing rights -- primarily because they are collected and administered by the performance rights organizations whose entire raison d'etre is to make sure that copyright holders get paid when their works are used by others.
If you give up your ownership rights in a song that you write, you give up this important source of income that will keep you very comfortable indeed if your song becomes a hit. Don’t give up your copyright lightly. Be sure you understand exactly what rights you are giving away as part of the record deal -- before you sign!