© 2015 Article funded by SCOAP3 and published under licence by Chinese Physical Society. The product of the Λ0b(B0) differential production cross-section and the branching fraction of the decay Λ0bJ= pK.. (B0!J= K Λ (892)0) is measured as a function of the beauty hadron transverse momentum, pT, and rapidity, y. The kinematic region of the measurements is pT >20 GeV=c and 2:0>y>4:5. The measurements use a data sample corresponding to an integrated luminosity of 3fb..1 collected by the LHCb detector in pp collisions at centre-of-mass energies ps = 7 TeV in 2011 and ps = 8 TeV in 2012. Based on previous LHCb results of the fragmentation fraction ratio, fΛ0 b =fd, the branching fraction of the decay Λ0 b!J= pK.. is measured to be B(Λ0 bJ= pK..)=(3:17±0:04±0:07±0:34+0:45 ..0:28 )10..4 ; where the first uncertainty is statistical, the second is systematic, the third is due to the uncertainty on the branching fraction of the decay B0J= K Λ (892)0, and the fourth is due to the knowledge of fΛ0 b =fd. The sum of the asymmetries in the production and decay between Λ0 b and Λ 0 b is also measured as a function of pT and y. The previously published branching fraction of Λ0 b ! J= p.., relative to that of Λ0 b ! J= pK.., is updated. The branching fractions of Λ0 b!P+ c (!J= p)K.. are determined.