The conditioning for all types of grappling could be done in various different ways.
Using Olympic bars, kettlebells, dumbbells, Bulgarian Bag, battle ropes and etc.
But there is one strength and conditioning protocol, that is constantly overlooked by many- using the weight of a partner, with or without resistance.
This is quite strange, since in the end, a training partner could be the closest thing to simulate any type of grappling match and using his body weight is the best way to get use to lift, move, throw and control a human body.
For static exercises, such as squats, dead lifts, overhead or bench press, we could use a partner with similar weight.
For ballistic exercises, here is one great suggestion:
Here I lift my son for a single hand overhand press:
Normal warming up session before any type of grappling class should consist on such exercises, including piggyback carry, fireman carry, princess carry and various lifts to carry a partner, using only our hand grip.
Here is is one old school Soviet video on conditioning of Greco- Roman wrestling, where many of the exercises could be found:
And here are just some people, having fun during workout 🙂