  In this paper, we investigate the heavy quark (HQ) mass effects on the
transverse momentum dependent fragmentation function (TMDFF). We first
calculate the one-loop TMDFF initiated by a heavy quark. We then investigate
the HQ TMDFF in the limit where the transverse momentum, $q_\perp$ is small
compared to the heavy quark mass, $q_\perp \ll m$ and also in the opposite
limit where $q_\perp \gg m$. As applications of the HQ TMDFF, we study the HQ
transverse momentum dependent jet fragmentation function, where the heavy quark
fragments into a jet containing a heavy hadron, and we investigate a heavy
hadron's transverse momentum dependent distribution with respect to the thrust
axis in $e^+e^-$ collisions.
