Let $f:X\to Y$ be a proper surjective holomorphic map between two $n$-dimensional connected complex manifolds $X$ and $Y$. $X$ is called a proper modification of $Y$ if there are nowhere dense compact analytic subsets $E\subset X$ and $S\subset Y$ such that the following hold:


(1) $f(E)\subset S$.
(2) $f$ maps $X\setminus E$ biholomorphically onto $Y\setminus S$.
(3) Every fibre $f^{-1}(y)$, $y\in S$, consists of more than one point.


Let $f:X\to\mathbb{C}^{n}$ be a proper modification of $\mathbb{C}^{n}$. Is $X$ necessarily an iterated blowup of $\mathbb{C}^{n}$ at finitely many points?



Proper modifications of $\mathbb{C}^{n}$
No. A counterexample to your question is given by a blow-up at point in $\mathbb C^n$ followed by a blow-up along a compact submanifold contained in the exceptional divisor of the first blow-up.


