  In 1984, Thomassen conjectured that for every constant $k \in \mathbb{N}$,
there exists $d$ such that every graph with average degree at least $d$
contains a balanced subdivision of a complete graph on $k$ vertices, i.e. a
subdivision in which each edge is subdivided the same number of times.
Recently, Liu and Montgomery confirmed Thomassen's conjecture. We show that for
every constant $0<c<1/2$, every graph with average degree at least $d$ contains
a balanced subdivision of a complete graph of size at least $\Omega(d^{c})$.
Note that this bound is almost optimal. Moreover, we show that every sparse
expander with minimum degree at least $d$ contains a balanced subdivision of a
complete graph of size at least $\Omega(d)$.
