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In this paper we study some properties of a totally $*$-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally $*$-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally $*$-paranormal operators through the local spectral theory. Finally, we show that every totally $*$-paranormal operator satisfies an analogue of the single valued extension property for $W^2(D,H)$ and some of totally $*$-paranormal operators have scalar extensions....