Most Geffen releases were distributed by various divisions of BMG, and later by Universal themselves. There is not much interesting to say about major label distribution, so this document primarily investigates the companies which distributed the Sub Pop and Tupelo releases.
Alternative Distribution Alliance was formed in 1993 by Warner Music Group (WMG) and Sub Pop, which owns 95% and 5% respectively [1,2], to focus on the independent music market. (WMG also aquired 49% of Sub Pop in 1995 [3a].) ADA UK was formed in 2006 to distribute independent music labels in Europe [1,2].
Before ADA, Sub Pop was mostly distributed by Caroline Distribution. Releases which claim to be distributed by Caroline should have been released before 1993, though the Caroline credit was not always removed when pressing reissues, so it is not always certain. On a reissue of Sub Pop 200 (SP25b), an ADA sticker was placed on the back insert, partly covering "Distributed exclusively by Caroline inc.", as seen in image 1. Sub Pop is still distributed by ADA in the USA.
1. ADA sticker covering old distribution credits
In the early 80's there was a boom in independent labels in the UK. The major labels were ignoring the bands who were creating music "alternative" to what the majors wanted. These bands were instead signing to local labels, formed either by local record retailers, the bands themselves, or their management. These labels needed to get their records into the record shops nationally. Regional distributors sprang up, each offering manufacturing and distribution deals to these new "alternative" labels. Record retailers did not want to buy from seven or eight small distributors so each of these small local distributors started offering each others' releases to the retailers in their geographical area. This meant that stock was held in each distributors' warehouse and each distributor had its own sales team. It also formed the foundations of the Cartel. 
The main Cartel members were Rough Trade, Backs, Nine Mile, Revolver, Red Rhino and Fast Forward. Rough Trade had a string of hits with The Smiths making them cash rich enough to buy a large warehouse in Collier Street in the Kings Cross area of London. The Smiths also saw the need for every record retailer to stock Cartel distributed product and no longer leave it to the small independent retailers. As more high street retailers opened accounts with the Cartel more and more independently distributed recordings became available through mainstream retailers. Many of these retailers provided sales information for the chart pollsters gallup and so more indie releases featured in the charts, generating airplay and more sales. 
The increasing success meant a restructuring of the Cartel. The regional distributors only provided stock to Rough Trade and it was dispatched from London to the retailers. The regional sales offices were retained and forwarded the orders to Rough Trade for distribution. The regional distributors concentrated on signing independent labels to manufacturing and distribution deals and the product was distributed by the newly formed Rough Trade Distribution. 
Cartel/ Rough Trade Distribution had a sales force of representatives who called on the retailers and presold forthcoming releases to the shops. The representatives brought test pressings to allow the retailers to decide what to order. Test pressings of a release being worked by the sales team would usually go to each of the ten sales representatives and to each of the six sales offices. Each would receive a sheet with release information, but may have received more than one test pressing. 
Tupelo's operations in the UK were handled by their distributor, Revolver , and Revolver used test pressings as described above. Their usual order of test pressings was 25 for a release that they thought would sell well, 12 if they thought they would only sell 1000-2000 copies, and 3-6 for small 1000 run pressing .
This applies to the Nirvana test pressings on Tupelo; Bleach, Blew, and Sliver 7". The Sliver 12" white labels were probably also used for regular promotion, in other words for radio play and the music press.
A K Records sticker as seen in image 2 can be found on some of the original plastic sleeves that the Love Buzz 7" singles came in. According to Calvin Johnsen, the founder of K Records, they distributed at least 50 copies of Love Buzz, probably more. It was listed in a few issues of K News, their newsletter and mail order catalog. K Records helped distribute a lot of the early Sub Pop catalog. 
2. K Records sticker
UNI Distribution was MCA's music distribution network, and they distributed many Geffen releases. After Seagram's purchase of MCA in 1995, UNI Distribution was renamed Universal Music & Video Distribution, Inc. In June 2001, it was renamed Universal Music & Video Distribution, Corp. It was changed again in 2006 to Universal Music Distribution. [3b]
UNI Records was also the name of a record label owned by MCA, and should not be confused with UNI Distribution. The label was active from 1966 to 1973, and briefly revived from 1988 to 1989. [3b]