Let $X$ be a smooth weak Fano but not Fano $3$-fold ($-K\_X$ is nef and big but not ample). Then the anti-canonical morphism $\phi:X\rightarrow W$ (the morphsim induced by the linear system $|-mK\_X|$ some $m\gg 0$) induces is a birational contraction. 


Assume that $\phi$ contracts a divisor. Could such divisor be contracted to a point or must it be necessarily contracted to a curve?



Anti-canonical divisorial contractions of weak Fano $3$-folds
What about taking the following example: consider $\mathbb P^1$ bundle over $\mathbb P^2$ given by the projectivisation of $\mathbb P(O\oplus O(-3))$ over $\mathbb P^2$. The linear system $-mK\_X$ contracts $\mathbb P^2$ to a point. 


