Consider the partial linear model Y = Xβ + g(T) + e. Where Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref.[1,2], it was proved that the estimator ∑ n * ≡ ( θ n * ) - 2 E n * ( ∑ n * ≡ ( θ n * ) - 2 E ˆ n * ) for the asymptotic variance of β n * ( β ˆ n * ) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for E n * and obtain the convergent rates for E ˆ n * and the strong uniform convergent rates for g ⌢ n * ( g n * ) .