  In this work, we discuss: (i) The ratios of different parton distribution
functions (PDFs), i.e., MMHT2014, CJ15, CTEQ6l1, HERAPDF15, MSTW2008, HERAPDF20
and MSHT20, and the corresponding Kimber-Martin-Ryskin (KMR) unintegrated
parton distribution functions (UPDFs) sets versus the hard scale $Q^2$, to find
out the sensibility of the KMR UPDFs with respect to the input PDFs sets. It is
shown that there is not much difference between the different input-PDFs or
corresponding UPDFs sets ratios. (ii) Then, the dependence of proton
$k_t$-factorization structure functions on the different UPDFs sets which can
use the above PDFs sets as input, are presented. The results are compared with
the experimental data of ZEUS, NMC and H1+ZEUS at the hard scale $Q^2 =27$ and
$90$ $GeV^2$, and a reasonable agreement is found, considering different input
PDFs sets. (iii) Furthermore, by fitting a Gaussian function, which depends on
the transverse momentum $k_t$, to the KMR UPDFs and averaging over $x$ (the
fractional parton momentum), we obtain the average transverse momentum,
$<k_t^2>$, in the scale range $Q^2=2.4-1.44\times10^4$ $GeV^2$, which is in
agreement with the other groups predictions, $0.25-0.44$ $GeV^2$ at $Q^2=2.4$
$GeV^2$. (iv) Finally we explore the average transverse momentum for which, the
results of proton structure function with the KMR UPDFs and that of the
Gaussian $k_t$-dependent, are consistent to each other. Through the above
report, at each step the parton branching (PB) UPDFs, i.e., the transverse
momentum dependent PDFs (PB TMDPDFs) are considered for comparisons with the
corresponding KMR UPDFs output.
