  The Vlasov-Nordstr\"{o}m-Fokker-Planck system describes the evolution of
self-gravitating matter experiencing collisions with a fixed background of
particles in the framework of a relativistic scalar theory of gravitation. We
study the spatially-homogeneous system and prove global existence and
uniqueness of solutions for the corresponding initial value problem in three
momentum dimensions. Additionally, we study the long time asymptotic behavior
of the system and prove that even in the absence of friction, solutions possess
a non-trivial asymptotic profile. An exact formula for the long time limit of
the particle density is derived in the ultra-relativistic case.
