  We investigate the impact of a high-degree vertex in Tur\'{a}n problems for
degenerate hypergraphs (including graphs). We say an $r$-graph $F$ is bounded
if there exist constants $\alpha, \beta>0$ such that for large $n$, every
$n$-vertex $F$-free $r$-graph with a vertex of degree at least $\alpha
\binom{n-1}{r-1}$ has fewer than $(1-\beta) \cdot \mathrm{ex}(n,F)$ edges. The
boundedness property is crucial for recent works~\cite{HHLLYZ23a,DHLY24} that
aim to extend the classical Hajnal--Szemer\'{e}di Theorem and the anti-Ramsey
theorems of Erd\H{o}s--Simonovits--S\'{o}s.
  We show that many well-studied degenerate hypergraphs, such as all even
cycles, most complete bipartite graphs, and the expansion of most complete
bipartite graphs, are bounded. In addition, to prove the boundedness of the
expansion of complete bipartite graphs, we introduce and solve a
Zarankiewicz-type problem for $3$-graphs, strengthening a theorem by
Kostochka--Mubayi--Verstra\"{e}te~\cite{KMV15}.
