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Theaters get to keep about 10% or around $1 per ticket on average for the first 2 weeks of release (during that time, with the big crowds, they make there money on concessions and on screen ads). Each week after the initial 2 weeks of release the % the theater gets to keep is increased. Specific details may be a little different from company to company but its generally the same for all the major studios and theaters country wide.

Now for the Distributor and Producer, when the movie is made buy an independent producer, there are usually 2 ways it can happen. The distributor buys the total rights to the movie or buys the rights to distribute for a specific area (say North America) for a set cost with the distributor getting all the profits from screening (this usually includes ancillary rights also), sometimes with a stipulation that if the movie makes over a certain amount the producer gets a %. The other way is that they share in the profits. The first way is much more common.

It is then the distributors responsibility to market it and chose the screen count buy sending reels to theaters. A reel print costs about $2000 each and a new digital version that some theaters are using costing about $5,500.

Major distributors like Universal have contracts with theater chains, so that they have screens on call whenever they need them. If Universal asks for 2000 screens for opening week, the theaters must give it to them. I think Disney has the most screens under contract, over 8000. Independent theaters go through and contract with a distributors buying agent, usually getting a little worse of a deal.

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In the UK the system is totaly different where it does have something to do with renting prints.

The simple reason is Universal didnt have confidence in the movie, its why they released it on a terrible date and made little effort to promote it.