  We present the first simultaneous measurement of the interaction rates of
$pp$, $^7$Be, and $pep$ solar neutrinos performed with a global fit to the
Borexino data in an extended energy range (0.19-2.93)$\,$MeV. This result was
obtained by analyzing 1291.51$\,$days of Borexino Phase-II data, collected
between December 2011 and May 2016 after an extensive scintillator purification
campaign. We find:
rate($pp$)$\,$=$\,$$134$$\,$$\pm$$\,$$10$$\,$($stat$)$\,$$^{\rm +6}_{\rm
-10}$$\,$($sys$)$\,$cpd/100$\,$t,
rate($^7$Be)$\,$=$\,$$48.3$$\,$$\pm$$\,$$1.1$$\,$($stat$)$\,$$^{\rm +0.4}_{\rm
-0.7}$$\,$($sys$)$\,$cpd/100$\,$t, and
rate($pep$)$\,$=$\,$$2.43$$\pm$$\,$$0.36$$\,$($stat$)$^{+0.15}_{-0.22}$$\,$($sys$)$\,$cpd/100$\,$t.
These numbers are in agreement with and improve the precision of our previous
measurements. In particular, the interaction rate of $^7$Be $\nu$'s is measured
with an unprecedented precision of 2.7%, showing that discriminating between
the high and low metallicity solar models is now largely dominated by
theoretical uncertainties. The absence of $pep$ neutrinos is rejected for the
first time at more than 5$\,$$\sigma$. An upper limit of $8.1$$\,$cpd/100$\,$t
(95%$\,$C.L.) on the CNO neutrino rate is obtained by setting an additional
constraint on the ratio between the $pp$ and $pep$ neutrino rates in the fit.
This limit has the same significance as that obtained by the Borexino Phase-I
(currently providing the tightest bound on this component), but is obtained by
applying a less stringent constraint on the $pep$ $\nu$ flux.
