Three Chokes from Side Control
The standard mount and back mount positions are usually seen as the most dominant of all positions in jiu jitsu. Both afford a wide variety of attack options for chokes and various limb attacks. These two positions have the most value in terms of BJJ point competitions, with each earning 4 points in the majority of competitions.
It can be argued that side mount or side control is a more dominating and more devastating position for a few reasons as described below:
Less Concern for the Hips
In standard mount, ideally my knees are as high up in the opponent's armpits as they can get in a high mount position. But the majority of the person's efforts are going to be to try to create space and block your adjustment so they can get their hips underneath of you. Once they have their hips beneath your hips, you must constantly be wary of being unbalanced to either side or chasing them as they get to their side and begin another attempt at escaping. In back mount, it's important for us to stay as attached to their hips as possible. Once attached whether with both hooks in or perhaps on our sides controlling a single hip with our legs, the lower half of our body is taken out of the attack equation.
In side control, you don't have to worry about their hips unbalancing you. Sometimes with just your arm, you are able to control them shrimping away or trying to turn away from you. This allows you to better focus your pressure on the upper third of their body creating reactions that lead to chokes or other submissions.
More Mobility for attacks
By not having your hips in danger of being unbalanced in standard mount and also not having them attached like they are in the back mount position, this keeps them free and gives you more mobility. From a standard side control position with both knees against your opponent who is flat on their back, controlling their hips at one end and their upper torso with your other knee, you can quickly leap up into a very painful and controlling knee on the belly position. You can adjust very easily a full 360 degrees around your opponent and with a few minor adjustments, be attacking from the opposite side quickly before they can even turn to a more favorable position.
Sneaky Gi Lapel Choke with Renzo Gracie
In this video, Master Renzo Gracie uses distraction to sneak his lapel around the far side of his opponent's neck. Then by adjusting his knees by bringing up his far knee to where the near knee was and driving his head down to the opponent's hips while extending his arm, he achieves the choke.
Spin Choke with Kurt Osiander
In this video, Kurt Osiander demonstrates a simple spin choke as well as a counter should the opponent properly defend the first choke. The spin choke is devastating, but the bread cutter counter to it's defense can be even more deadly.
Side Control to Knee on Belly and Step Over Choke with Robson Moura
In the video below, Robson Moura shows a sneaky variation of the step over choke launched from knee on the belly.
Chokes from side control are some of the most effective and easiest techniques to build into your arsenal. Side control is a very multi-faceted position that can greatly frustrate opponents and cause them to not be as cognizant of the new attacks you've added to your game.
For an in depth article which describes several variations of head and arm chokes, each with variations that can be attacked from side control, check out this article from BJJ Fanatics.
If you want to explore chokes in more detail, you will definitely want to check out BJJ Black Belt and Judo Olympian Travis Steven's Choke DVD instructionals here.