to spread  - difundirse, correr, propagarse, esparcir, extenderse, untar (mantequilla, etc.), difundir, sembrar, propagar 

to circulate  - circular, circular (noticias, etc.), hacer circular, divulgar 

to divulge  - revelar, divulgar 

to reveal  - revelar, divulgar, manifestar, mostrar, dejar ver 

to popularize  - popularizar