We find the minimal free resolution of a fat star-configuration 핏 in ℙn of type (r,s,t) defined by general forms of degrees d1, ..., dr, and show that a fat linear star-configuration 핏 in ℙ2 never has generic Hilbert function if (s,t) ≠ (1,1) or (2,2). These two results generalize the interesting results of [2].