Bottlebrush polymers contain polymeric side-chains attached to a linear polymer backbone, and they are currently of interest for a variety of potential applications that include drug delivery, tailored surface wettability, and self-assembled photonics. These polymers are challenging to synthesize in large quantities, so for practical applications, it is of interest to study their properties as additives for low-cost linear polymers. In this work, we examine the phase behavior of bottlebrush polystyrene (PS) and linear deuterated polystyrene (dPS) in thin films. These nearly athermal systems exhibit wetting and dewetting transitions that drive bottlebrush dispersion or aggregation, respectively, and these effects depend on the relative degrees of polymerization of matrix chains N-m to those of bottlebrush side-chains N-sc. When N-m/(sc) is low (<= 1.6), the bottlebrushes are dispersed throughout the film thickness with a slight excess at the free surface and substrate interfaces. When N-m/N-sc is high (>= 8), the bottlebrushes are depleted from the interior of the film and strongly segregated at the interfaces. The interfacial excess is driven by an entropic depletion attraction effect: larger branched molecules are adsorbed (attracted) to the interfaces, and the linear chains are displaced to the film's interior where they gain conformational entropy. The bottlebrushes prefer to accumulate at the silicon substrate over the air interface, and this may be driven by the more restrictive condition of a hard boundary or weak van der Waals interactions with the underlying silicon. These studies demonstrate that low concentrations of certain bottlebrush polymer architectures can generate brushlike surfaces and interfaces in any thermoplastic material through a spontaneous, entropy-driven segregation process.