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SpaceX's drone ships have a vehicle that drives under a booster after landing and then clamps onto it to secure it. Photos of it suggest that it has neither ballast nor any way to clamp onto the drone ship.
So how heavy is it, compared to a landed and thus low-on-fuel booster? How heavy would it have to be to stay fairly motionless despite wind loads, deck tilting, and ship maneuvers?
(Here's a detailed history of the Octagrabbers.)
Bottom line: Octograbber is dead weight ballast that lowers the Falcon9 center of gravity. No rare earth magnets, suction cups or Velcro are needed.
Dry mass of Falcon9 1st stage is 25,600kg. About 5000kg of this is the 9 Merlin engines and the landing legs. This would put the center of mass roughly 1/3 up the vertical length.
The Octagrabber is very heavily built. This photo shows the base plate about 10cm thick, assuming the road tires are 1 meter in diameter (some of the thickness is I-beam flange).
The area of the Octagrabber is about 150 m^2, assuming the figure in the photo is 180cm tall
If we model the Octagrabber as a 10cm thick steel plate with an area of 150m^2, and a density of 7.7 tons/m^2, that gives a mass of 120,000 kg. Clamped to the Falcon9, this gives a low enough CM the assembly ain't going nowhere.
of course, this is a estimate. But it is in line with the load capacity of the pneumatic tires on the dolly. 18 pairs of tandem wheels with 500lb capacity per inch of tread width gives 160,000kg capacity for that dolly.
Point is, the designers of Octograbber can lower the CM of the assembly as low as they desire with enough dumb steel. It only needs to keep Falcon9 vertical until the crew comes aboard and chains it to the hard points on the deck
I would imagine it's a combination of weight (lowering the booster's centre of gravity) and energised magnetic attachment to the steel deck (either from the Octagrabber itself, or from under the deck).
The dry mass of a F9 first stage is 25.6 tonnes (lets say 26 tonnes after landing with residual propellant on board).
In the images I've seen, there's a power/control cable extending from the Octagrabber to the side of the barge it's deployed from. This could not only provide the means to power and control the device as it moves under the booster, but also actuate neodymium magnets that would secure it to the deck without damaging the deck from welding.
