From a total data sample of 701.1 pb^-1 recorded with e+e- centre-of-mass energies of sqrt = 161-209 GeV with the OPAL detector at LEP, 11693 W-pair candidate events are selected. These data are used to obtain measurements of the W-pair production cross sections at 10 different centre-of-mass energies. The ratio of the measured cross sections to the Standard Model expectation is found to be: data/SM = 1.002 +- 0.011(stat.) +- 0.007(syst.) +- 0.005(theory), where the uncertainties are statistical, experimental systematics and theory systematics respectively. The data are used to determine the W boson branching fractions, which are found to be consistent with lepton universality of the charged current interaction. Assuming lepton universality, the branching ratio to hadrons is determined to be 67.41 +- 0.37(stat.) +- 0.23(syst.)%, from which the CKM matrix element Vcs is determined to be 0.96+-0.017(stat.)+-0.012(syst.). The differential cross section as a function of the W^- production angle is measured for the qqev and qqmv final states. The results described in this paper are consistent with the expectations from the Standard Model.

Elements of the spin density matrix for W bosons in e+e- -> W+W- -> qqln events are measured from data recorded by the OPAL detector at LEP. This information is used calculate polarised differential cross-sections and to search for CP-violating effects. Results are presented for W bosons produced in e+e- collisions with centre-of-mass energies between 183 GeV and 209 GeV. The average fraction of W bosons that are longitudinally polarised is found to be (23.9 +- 2.1 +- 1.1)% compared to a Standard Model prediction of (23.9 +- 0.1)%. All results are consistent with CP conservation.

These final results on e+e- -> W+W- production cross-section measurements at LEP2 use data collected by the DELPHI detector at centre-of-mass energies up to 209 GeV. Measurements of total cross-sections, W angular differential distributions and decay branching fractions, and the value of the CKM element |V_{cs}| are compared to the expectations of the Standard Model. These results supersede all values previously published by DELPHI.

From a data sample of 183 pb^-1 recorded at a center-of-mass energy of roots = 189 GeV with the OPAL detector at LEP, 3068 W-pair candidate events are selected. Assuming Standard Model W boson decay branching fractions, the W-pair production cross section is measured to be sigmaWW = 16.30 +- 0.34(stat.) +- 0.18(syst.) pb. When combined with previous OPAL measurements, the W boson branching fraction to hadrons is determined to be 68.32 +- 0.61(stat.) +- 0.28(syst.) % assuming lepton universality. These results are consistent with Standard Model expectations.

The cross-section for the process e+e- -> W+W- has been measured with the data sample collected by DELPHI at an average centre-of-mass energy of 189 GeV and corresponding to an integrated luminosity of 155 pb^{-1}. Based on the 2392 events selected as WW candidates, the cross-section for the doubly resonant process e+e- -> W+W- has been measured to be 15.83 +- 0.38 (stat) +- 0.20 (syst) pb. The branching fractions of the W decay were also measured and found to be in good agreement with the Standard Model expectation. From these a value of the CKM mixing matrix element |V_{cs}| = 1.001 +- 0.040 (stat) +- 0.020 (syst) was derived.

The production of W-pairs is analysed in a data sample collected by ALEPH at a mean centre-of-mass energy of 188.6 GeV, corresponding to an integrated luminosity of 174.2 pb^-1. Cross sections are given for different topologies of W decays into leptons or hadrons. Combining all final states and assuming Standard Model branching fractions, the total W-pair cross section is measured to be 15.71 +- 0.34 (stat) +- 0.18 (syst) pb. Using also the W-pair data samples collected by ALEPH at lower centre-of-mass energies, the decay branching fraction of the W boson into hadrons is measured to be BR (W > hadrons) = 66.97 +- 0.65 (stat) +- 0.32 (syst) %, allowing a determination of the CKM matrix element |V(cs)|= 0.951 +- 0.030 (stat) +- 0.015 (syst).

From a data sample of $9.98 {\mathrm{ pb^{-1}}}$ integrated luminosity, collected by DELPHI at a centre-of-mass energy of 172 GeV, 118 events were selected as W-pa

The e + e − → W + W − cross section is measured in a data sample collected by ALEPH at a mean centre-of-mass energy of 172.09 GeV, corresponding to an integrated luminosity of 10.65 pb −1 . Cross sections are given for the three topologies, fully leptonic, semi-leptonic and hadronic of a W-pair decay. Under the assumption that no other decay modes are present, the W-pair cross section is measured to be 11.7±1.2 (stat.) ±0.3 (syst.) pb . The existence of the triple gauge boson vertex of the Standard Model is clearly preferred by the data. The decay branching ratio of the W boson into hadrons is measured to be B(W→hadrons) =67.7±3.1 (stat.) ±0.7 (syst.) % , allowing a determination of the CKM matrix element | V cs |=0.98±0.14(stat.)±0.03(syst.).

A study of W-pair production in e+e- annihilations at Lep2 is presented, based on 877 W+W- candidates corresponding to an integrated luminosity of 57 pb-1 at sqrt(s) = 183 GeV. Assuming that the angular distributions of the W-pair production and decay, as well as their branching fractions, are described by the Standard Model, the W-pair production cross-section is measured to be 15.43 +- 0.61 (stat.) +- 0.26 (syst.) pb. Assuming lepton universality and combining with our results from lower centre-of-mass energies, the W branching fraction to hadrons is determined to be 67.9 +- 1.2 (stat.) +- 0.5 (syst.)%. The number of W-pair candidates and the angular distributions for each final state (qqlnu,qqqq,lnulnu) are used to determine the triple gauge boson couplings. After combining these values with our results from lower centre-of-mass energies we obtain D(kappa_g)=0.11+0.52-0.37, D(g^z_1)=0.01+0.13-0.12 and lambda=-0.10+0.13-0.12, where the errors include both statistical and systematic uncertainties and each coupling is determined setting the other two couplings to the Standard Model value. The fraction of W bosons produced with a longitudinal polarisation is measured to be 0.242+-0.091(stat.)+-0.023(syst.). All these measurements are consistent with the Standard Model expectations.

The production of W+W- pairs is analysed in a data sample collected by ALEPH at a mean centre-of-mass energy of 182.7 GeV, corresponding to an integrated luminosity of 57 pb-1. Cross sections are given for different topologies of W decays into leptons or hadrons. Under Standard Model assumptions for the W-pair production and decay, the W-pair cross section is measured to be 15.57+-0.62(stat.)+-0.29(syst.) pb. Using also the W-pair data samples collected by ALEPH at lower centre-of-mass energies, the decay branching ratio of the W boson into hadrons is measured to be B(W->hadrons)= 68.93+-1.21(stat.)+-0.51(syst.)%, allowing a determination of the CKM matrix element |Vcs|= 1.043 +- 0.058(stat.) +- 0.026(syst.). The agreement of the cross sections with the Standard Model prediction allows a limit to be set on the W decay rate to undetectable final states.