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In this paper we shall study the growth and asymptotic behaviour of sub-harmonic functions of order greater than half near Polya peaks. In some way our result is a generalization of Paley\'s conjecture. The method employed is a non-asymptotic via a normal family of subharmonic functions. Key words/phrases : Order, Polya peaks, star function, subharmonic SINET: Ethiopian Journal of Science Vol. 27 (2) 2004: 93-97

Growth of subharmonic functions of order greater than half