Can parameters other than $n$ be always ignored in big $O$ notation?
In general you cannot erase things. A bivariate function $f$ is $O((n+k)\log n)$ if there exists a constant $C&gt;0$ such that for all legal settings of the parameters $n,k$, we have $f(n,k) \leq C(n+k)\log n$. Here a setting of parameters is legal if it can actually happen – for example, if $V,E$ are the number of vertices and edges in a simple graph, then we always have $E \leq V(V-1)/2$, any other setting being illegal. If in some context you know that $k \leq Bn$, then in that context (which restricts the set of legal settings of parameters) $f = O(n\log n)$. In any other context, you cannot drop the $k$.

In your particular case, the Bentley–Ottmann algorithm, it is generally not the case that $k = O(n)$, and so $k$ cannot be dropped.