The main aim of this paper is to gove an extencion of the charcterisation given in [18] of finite posetsJhaving only finitely many isomorphism classes of indecomposable socle projectiveK-linear representations over a given fieldK. The characterisation is given in Theprem 1.2 and in Theorem 4.1 in terms of the Tits quadratic form associated toJ, in terms of the endomorphism rings and self-extensions of indecomposable representations, and in terms of the infinitd radical of the category prin(KJ). A converse to a theorem of Bongartz [4] is given in Corollary 3.5.