RTO, ok first of all be go minded, too many accidents have occured from RTO beyond V1, even some with the nose gear off the ground.
From 1959 to 1990 there have been 74 RTO overrun accidents in western jet aircraft, resulting in 400 fatalities, 58 % of theese the RTO was initiated above V1.
The Captain has to guard the Thrust Levers, since it is ultimately his responsibility to decide stop or go, even if the FO is PF, and in my experience there is no problem in taking over the controls form the FO.
Especially with new FO´s they tend to have less excess capacity to analyze the situation during TO.
The main stopping agent in an RTO is the wheel brakes, manually or autobrake in RTO, these must be used maximum all the way till the aircraft comes to a "rocking stop"
Next comes reverse and spoilers, the spoilers increase drag, but more significantly increases weight on wheels thus increasing brake performance.
Thus a tire burst before V1 should NOT lead to a RTO, since the stopping capability with a damaged tyres is next to none, and an overrun is almost certain. On the other hand a prepared landing with damaged tyres, can performed safely.
RTO is a complex decision, with only litte time available, naturally it is the Commanders.
KG