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Given a domain of holomorphy $D$ in $\mathbb{C}^N$, $N\geq 2$, we show thatthe set of holomorphic functions in $D$ whose cluster sets along any finitelength paths to the boundary of $D$ is maximal, is residual, densely lineableand spaceable in the space $\mathcal{O}(D)$ of holomorphic functions in $D$.Besides, if $D$ is a strictly pseudoconvex domain in $\mathbb{C}^N$, and if asuitable family of smooth curves $\gamma(x,r)$, $x\in bD$, $r\in [0,1)$, endingat a point of $bD$ is given, then we exhibit a spaceable, densely lineable andresidual subset of $\mathcal{O}(D)$, every element $f$ of which satisfies thefollowing property: For any measurable function $h$ on $bD$, there exists asequence $(r_n)_n \in [0,1)$ tending to $1$, such that  \[  f\circ \gamma(x,r_n) \rightarrow h (x),\,n\rightarrow \infty,  \] for almost every $x$ in $bD$.

Wild boundary behaviour of holomorphic functions in domains of $\mathbb{C}^N$