The understanding of size-dependent properties is key to the implementation of nanotechnology. One controversial and unresolved topic is the influence of characteristic size on the glass transition temperature (T(g)) for ultrathin films and other nanoscale geometries. We show that T(g) does depend on size for polystyrene spherical domains with diameters from 20 to 70 nm which are formed from phase separation of diblock copolymers containing a poly(styrene-co-butadiene) soft block and a polystyrene hard block. A comparison of our data with published results on other block copolymer systems indicates that the size dependence of T(g) is a consequence of diffuse interfaces and does not reflect an intrinsic size effect. This is supported by our measurements on 27 nm polystyrene domains in a styrene-isobutylene-styrene triblock copolymer which indicate only a small T(g) depression (3 K) compared to bulk behavior. We expect no effect of size on T(g) in the limit as the solubility parameters of the hard and soft blocks diverge from each other. This strongly segregated limiting behavior agrees with published data for dry and aqueous suspensions of small polystyrene spheres but is in sharp contrast to the strong influence of film thickness on T(g) noted in the literature for free standing ultrathin polystyrene films.