  An interval colouring of a graph $G=(V,E)$ is a proper colouring $c\colon
E\to \mathbb{Z}$ such that the set of colours of edges incident to any given
vertex forms an interval of $\mathbb{Z}$. The interval thickness $\theta(G)$ of
a graph $G$ is the smallest integer $k$ such that $G$ can be edge-partitioned
into $k$ interval colourable graphs, and $\theta(n)$ is the largest interval
thickness over graphs on $n$ vertices. We show that $c \frac{\log n}{\log \log
n} \leq \theta(n) \leq n^{8/9+o(1)}$ for some $c>0$. In particular this answers
a question by Asratian, Casselgren, and Petrosyan.
  In the second part of the paper, we confirm a conjecture of Axenovich that
the maximum number of colours used in an interval colouring of a planar graph
on $n$ vertices is at most $3n/2-2$.
