There are three main forces fighting for traction. Braking, cornering and accelerating. You can’t slow down and speed up at the same time so braking and accelerating should never fight for available traction. However there can be a fight for traction between slowing down (braking) and cornering. The same with accelerating and cornering, they can both fight for available traction. Contact patch just adds to the dispute.
The contact patch of the tires are greatest when the bike is bolt upright, perpendicular to the surface and straight in line with the force of gravity. Braking and acceleration can be maximized here. Motorcycle tire design says that as the bike leans over the contact patch becomes smaller and smaller.
When you approach a corner you are probably perpendicular to the pavement and all traction is available for braking. As you start to turn into the corner, you begin to lean and you start to lose contact patch. You also start to introduce a lateral cornering force. Your available traction for braking is now decreasing. Cornering forces now want a piece of the traction pie. As lean angle eats more pie there’s less available for braking. ABS can help referee the fight but it can’t save all the pie. Cornering ABS is smart enough to sense lean angle and compensate by reducing the available brake power.
It is very important to properly judge your entrance speed and get most of your braking done before the turn in point. If you have misjudged your cornering speed and need more brakes it’s ok to grab a little more brakes while there is little to no lean angle. Applying the brakes while leaning has a tendancy to stand the bike up and increase the diameter of your turn. This can put you into oncoming traffic in a right corner and off in the rhubarb in a left hand corner. You definitely don’t want to be at maximum lean angle and decide you need brakes.
The apex can be defined as the transition point from slow to go. After the apex the fight transitions to from braking to accelerating. Braking force tag out and accelerating force jumps into the ring. If you apply the throttle too quickly while leaned over there may not be enough contact patch or traction available. Cornering still needs the traction. This can result in the classic high side crash. The best way out of the corner is for cornering to gently hand over the traction to acceleration as the contact patch increases. Contact patch increases as you decrease the lean angle. Traction control is an electronic aid designed to referee the fight to make sure no one gets tossed out of the ring.
In this battle for traction no one force reigns supreme. They have to work together and make the transitions as smooth as possible. On the race track you might push one force then the other to achieve maximum balance. On the street you just need to be smooth and make sure to judge your speed will in advance.