They're all made by Nissan with only minor ancillary parts by the others.
That changes next year though I believe.
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Small alteration

Renault make the vans and they are rebadged as Vauxhall and Nissan. But Nissan has a major share holding in Renault.
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Not on the info I found.
And the fact that there are Nissan badges on everything under the bonnet & battery.
Not a 'fact' as such, just what I found out while researching for mine.
The 2014 models are going to be made by Vauxhall and rebadged from what I found but mine is the mk3 I think...
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Got this from Wikepedia
"Second generation (2001–present)[edit]Second generation
Overview
Manufacturer Renault
Opel
Also called Nissan Primastar
Opel Vivaro
Vauxhall Vivaro
Production 2001–present
Model years 2001-present
Body and chassis
Class Van, Minibus
Body style 4-door minivan
2-door pickup truck
Powertrain
Engine 1,870 cc (1.9 L) dCi 100PS I4
1,995 cc (2.0 L) dCi DOHC 90PS/115PS I4
2,488 cc (2.5 L) dCi DOHC 150PS I4
1,997 cc (2.0 L) 120PS DOHC I4
Transmission 6-speed manual
6-speed Quickshift semi-automatic
Dimensions
Wheelbase SWB: 3,098 mm (122.0 in)
LWB: 3,498 mm (137.7 in)
Length SWB: 4,782 mm (188.3 in)
LWB: 5,182 mm (204.0 in)
Regular Pickup: 5,038 mm (198.3 in)
Crew Pickup: 5,438 mm (214.1 in)
Width 1,904 mm (75.0 in)
Height Crew Van: 1,380 mm (54.3 in)
SWB: 2,497 mm (98.3 in) & 2,400 mm (94.5 in)
LWB: 2,800 mm (110.2 in)
Pickup Regular: 1,966 mm (77.4 in)
Pickup Crew: 1,973 mm (77.7 in)
Chronology
Predecessor Renault Estafette
The current Trafic resulted from a joint venture between German Opel, Japanese Nissan and French Renault. It is also sold as an Opel Vivaro, Vauxhall Vivaro and by Nissan as the Primastar.
Designed by Renault's corporate design department based within the company's Technocentre outside Paris, the Trafic was developed by the engineering team of Renault's light commercial vehicle unit at Villiers-Saint-Fréderic. Manufactured by GM Manufacturing Luton at its plant in Luton—beside Primastar and the Vivaro—the Trafic was the first Renault vehicle to be built in the United Kingdom in more than 30 years.[5][6]
In an agreement between Renault and Nissan, versions of the van are also manufactured at Nissan's plant in Barcelona, Spain.[7]
The van exists in several versions, from a 3-seater with all the rear space available for loads, to a 9-seater. Its name is based on the French word for "trade" or "traffic" (depending on the context).
The van was designed by Renault in Paris, and both Renault and Opel versions are manufactured by Vauxhall at their plant in Luton.[7] In 2012, UK production of the Vivaro totalled 36,982 and 16,483 for the Renault Trafic.[8]
A mild facelift in 2006 saw the orange indicators swapped for clear ones more integrated into the headlamp housings. On the Vauxhall and Opel models, the indicators moved from the front bumpers, up into the headlamp housings, thus looking more similar to the Renault."
This same situation applies to other vans. The Citroen Relay and Peugeot Boxer are made by Fiat in Italy which are dirivatives of the Fiat Ducato.
PSA make the Dispatch and Expert in France which is rebadged as a Fiat Scudo.
Vauhall are also rebadging the Fiat Dobolo as their Combo.
Some of the 'genuine' parts I have bought for my Citroen Relay have come in Peugeot packaging.