Maybe not academically correct explanation, but the general idea:
With increasing degree of branching glass transition of the same polymer with the same average Mn tends to decrease.
In is much harder for branched structure to form a dense packed structure. As a result intermolecular interactions become weaker and energy requirement for phase transition decrease as well.
Therefore glass transition process could occur at lower temperature.
The same is true for melting point.
The greater degree of branching the harder it is for polymer to crystallize as well
the glass transition temperature depends on polymer chain ends. Thus branched polymers exhibit a lower Tg due to the additional chain ends. This dependency can be observed for polymers below their entanglement molecuar weight, for which Tg decreases with decreasing molecular weight, or for polymer with a ring topology, which express a comparably higher Tg due to the absence of chain ends.
It has to do with the mobility of the chain in non polar systems; the highly branched will have greater mobility, lower Tg. Article Effects of flexibility and branching of side chains on the m...