  The marked increase in advertisements over online social networks (OSNs)
necessitates the study of content propagation. We analyse the viral markets
with content providers competing for the propagation of similar posts over
OSNs. Towards this, we required a new variant of the branching process (BP),
which we named as "Branching process with attack"; the entities upon wake up
attempt to attack and acquire the opposite population; furthermore, each entity
produces its offsprings as is usually considered in BPs.
  In addition to providing expressions for the growth rates of individual
posts, dichotomy etc., we explore the co-existence of posts; can the competing
content spread and explode (number of unread/live copies of both posts grow
significantly with time) simultaneously over the network? We prove that either
one or both populations/posts get extinct or the populations settle to a unique
co-existence equilibrium and derive the corresponding asymptotic ratios of the
two populations/posts. Our analysis applies to large population networks
focusing on mass behaviour, rather than micro details. Our study provides
insights into two crucial design aspects, the number of seed users and the
quality of the post.
