[For part I see the author, Duke Math. J. 56, No. 1, 193-218 (1988; Zbl 0659.32005).] Let \(f:\mathbb{C}^ n\to X\) be a nondegenerate holomorphic map into a compact manifold of dimension \(n\). Let \(D\) be a divisor on \(X\) with the complexity \(k\). We define the differential form on \(\mathbb{C}^ n\) \[ \omega(z)=dd^ c\log\| z\|^ 2 \hbox{ and } \sigma(z)=d^ c\log\| z\|^ 2\land\omega^{n-1}, \] the mean proximity function \(m_{f,D}(r)\) of the radius \(r\) in \(\mathbb{C}^ n\), the counting function \(N_{f,D}(r)\), the height function \(T_{f,D}(r)\) and the ramification function \(N_{f,Ram}(r)\) as usual. The author gives an inequality the left hand-side of which concerns a signed sum of these and the right hand-side of which is \(\hbox{const}+{n\over 2} S(c T_ f ^{1+k/n})\). He conjectures that the exponent \(1+k/n\) is best possible. This is an improvement of Wong's result concerning \textit{J. A. Carlson} and \textit{P. Griffiths} [Ann. Math., II. Ser. 95. 557-584 (1972; Zbl 0248.32018)]. He also uses the Ahlfors technique as revised by Wong and gives a version up to the higher dimensional version still with weak error term given at page 70 of \textit{P. Griffiths} [Entire holomorphic mappings in one and several variables (Ann. Math. Studies, 85)(Princeton 1976; Zbl 0317.32023)] concerning the error term of the logarithmic derivative stated with a weak error term by Nevanlinna in dimension 1. He also defines and investigates Ric.