From a partial-differential eigenproblem, without use of dipole approximation, we show that the eigenmodes (surface plasmons) of disordered nanosystems (modeled as random planar composites) are not universally Anderson localized, but can have properties of both localized and delocalized states simultaneously. Their topology is determined by separate small-scale “hot spots” that are distributed and coherent over a length that may be comparable to the total size of the system. Coherence lengths and oscillator strengths vary by orders of magnitude from mode to mode at nearby frequencies. The existence of dark vs luminous eigenmodes is established and attributed to the effect of charge- and parity-conservation laws. Possible applications are discussed.