  We study electron-positron pair production in polar caps of energetic pulsars
to determine the maximum multiplicity of pair plasma a pulsar can produce under
the most favorable conditions. This paper complements and updates our study of
pair cascades presented in Timokhin & Harding (2015) with more accurate
treatment of the effects of ultra strong B>3x10^{12}G magnetic fields and
emission processes of primary and secondary particles. We include pairs
produced by curvature and synchrotron radiation photons as well as resonant
Compton scattered photons. We develop a semi-analytical model of
electron-positrons cascades which can efficiently simulate pair cascades with
an arbitrary number of microphysical processes and use it to explore cascade
properties for a wide range of pulsar parameters. We argue that the maximum
cascade multiplicity can not exceed ~ a few x 10^5 and the multiplicity has a
rather weak dependence on pulsar period on pulsar period. The highest
multiplicity is achieved in pulsars with magnetic field 4x10^{12}<B<10^{13}G
and hot surfaces, with T>10^6K. We also derive analytical expressions for
several physical quantities relevant for electromagnetic cascade in pulsars
which may be useful in future works on pulsar cascades, including the upper
limit on cascade multiplicity and various approximations for the parameter
\chi, the exponential factor in the expression for photon attenuation in strong
magnetic field.
