  The entanglement and localization in eigenstates of strongly chaotic
subsystems are studied as a function of their interaction strength. Excellent
measures for this purpose are the von-Neumann entropy, Havrda-Charv{\'
a}t-Tsallis entropies, and the averaged inverse participation ratio. All the
entropies are shown to follow a remarkably simple exponential form, which
describes a universal and rapid transition to nearly maximal entanglement for
increasing interaction strength. An unexpectedly exact relationship between the
subsystem averaged inverse participation ratio and purity is derived that
infers the transition in the localization as well.
