Let's say a morphism $f:X\to Y$ is compactifiable if it admits a factorization $f = pj$ with $j:X\to P$ an open immersion and $p:P\to Y$ proper.

In SGA 4 Exp. XVII, Deligne says that Nagata proved that any morphism of separated integral northerian schemes is compactifiable but that he didn't understand the proof.

My questions:

• Where can I find a proof that any algebraic morphism of quasi-projective varieties is compactifiable?
• What about the complex analytic setting? It seems it already breaks down for $\exp: \mathbb{C} \to \mathbb{C}^\times$? Is there a partial result?