  We discuss the upper limit, $k_{\text{max}}$, of the transverse-momentum
integration performed in the $k_t$-factorization formula. Based on explicit
calculations in the Yukawa theory and the study of seminal papers, we argue
that $k_{\text{max}}$ is equal to the factorization scale $\mu_F$ used to
factorize the cross section into an off-shell hard coefficient and a universal
factor. There is consequently a relation between $k_{\text{max}}$ and the
definition of unintegrated parton densities (UPDFs). The use of an inconsistent
relation leads potentially to the overestimation of the cross section, which
has been observed, e.g., in D-meson production. One of our conclusions is that
UPDFs related to collinear PDFs by an integration up to $\mu\sim Q$, where $Q$
is the hard scale and $\mu$ the scale in the collinear PDFs, imply that
$k_{\text{max}}^2 \sim Q^2$. Integrating the transverse-momentum significantly
above may result in the overestimation of the cross section. On the opposite,
for UPDFs related to the collinear ones by an integration of the transverse
momentum up to infinity, any $k_{\text{max}}^2 > Q^2$ is fine.
