Increasing returns, implications? If a firm has increasing returns to scale (i.e., doubling inputs more than doubles output) would that firm logically end up being the sole firm in its sector in the long run?
If not, what is the advantage of displaying IRTS?
Provided that increasing returns to scale apply over the whole production function of the company it is likely that it would become natural monopoly. For example, Mankiw in Principles of Economics (pp 292) in some passages even defines monopolies in relation to their cost  function:

When a firm’s average-total-cost curve continually declines, the
firm has what is called a natural monopoly.

Generally the average-total-cost curve will continually decline when firm has increasing returns to scale.
However, there are models with increased returns to scale where monopolies are not inevitable. For example, Wang (2016) presents a model of banking competition where firms face increasing returns to scale, and even though the model predicts increase in market concentration it does not necessary predict that a single bank will become monopoly.