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The PAMELA collaboration recently released the $e^+$ absolute spectrumbetween 1 and 300 GeV in addition to the positron fraction and the $e^-$spectrum previously measured in the same period. We use the newly developedthree-dimensional upgrade of the DRAGON package to model those data. This codeallows us to consider a realistic spiral arm source distribution in the Galaxy,which impacts the high-energy shape of the propagated spectra. At low energy wetreat solar modulation with the HelioProp code and compare its results withthose obtained using the usual force-field approximation. We show that allPAMELA data sets can be consistently, and accurately, described in terms of astandard background on top of which a charge symmetric $e^+$ + $e^-$ extracomponent with harder injection spectrum is added; this extra contribution ispeaked at about 1 - 10 TeV and may originate from a diffuse population ofsources located in the Galactic arms. For the first time, we compute the energyrequired to sustain such a relevant positron flux in the Galaxy, finding thatit is naturally compatible with an astrophysical origin. We considered severalreference propagation setups; we find that models with a low (or null)reacceleration - tuned against light nuclei data - nicely describe both PAMELAleptonic and hadronic data with no need to introduce a low-energy break in theproton and helium spectra, as it would be required for high reaccelerationmodels. We also compare our models with the preliminary $e^-$ and $e^+$absolute spectra recently measured by AMS-02. We find that those data,differently from what is inferred from the positron fraction alone, favor ahigh energy cutoff (about 10 TeV) of the extra component if this is uniquelygenerated in the Galactic arms. A lower cutoff may be allowed if a relevantcontribution from powerful $e^-$ + $e^+$ nearby accelerators is invoked.

PAMELA and AMS-02 positron and electron spectra are reproduced by three-dimensional cosmic-ray modeling