If Trump manages to collect 1305 delegates during the primaries, there will not be a brokered convention.
A brokered convention would exist only if none of the candidates accumulated 1305 delegates by the time of the convention.
If the current polling is a real indicator, Trump could likely have 1305 by mid-March.
Most of the southern states now have their primaries in early March, making them very influential. In previous years those primaries were late in spring, making them relatively uneventful, as the nominee was usually determined weeks earlier.
I believe he would have to have one majorities in 8 states and a majority of delegates to win on the first ballot.
If no one wins on the first ballot it would become a brokered convention.
My understanding is that the critical mass of delegates is not in the southern states.