Travel or Jump Ball?
 

What do you call?

A1 drives to basket, begins to gather ball, but defender puts hand on the ball (pins it) which causes A1 to take extra steps.

Have to see this type of play but as you said it's either a held ball or a travel. If the offensive player takes the extra steps in attempt to retain possession I likely go with the travel, otherwise it's to the arrow.

Held ball.

Easy held ball call; by definition the shot has begun and he's prevented from releasing it.

Pick Up, Dust Off ...
 

(Apologies to Frank Sinatra.)

A few other held ball, or travel, situations from the files of the Mythbusters:

When an airborne player keeps control of an attempted shot that is blocked and is unable to release the ball and returns to the floor with it, that player has not traveled; it is a held ball. If, in this situation, the shooter loses control of the ball because of the block, then this is simply a blocked shot and play continues. If, in this situation, the defender simply touches the ball, and the airborne shooter returns to the floor holding the ball, it’s a traveling violation. When an airborne player tries for goal, sees that the try will be blocked, purposely drops the ball, and picks up the ball after it hits the floor, that player has traveled by starting a dribble with the pivot foot off the floor.

Not so fast, sir! Is A1 an airborne player? ;)

(Hint: Check the definition of held ball.)

is a defenders hand pinning the ball equivalent to equal possesion?

Would you call this fully accurate...? (If not, why not?)

If the ball-holder picks up and sets down his pivot foot, it's a travel.

If the ball-holder picks up and sets down his pivot foot while a defender has his hand on the ball, it's a held ball.

Did the defender's hand on the ball prevent the player from releasing the ball?

Yeah, I realized that after I posted it, just forgot to come back and address it.

Okay, let's modify.

If the ball-holder picks up and sets down his pivot foot, while a defender's hand on the ball prevents the ball-holder from releasing it, it's a held ball.

How's that?

By pure definition? No. As Nevada notes, check out the definition of held ball. Should be in rule 4 somewhere.

1) Yes.

2) On a rules test? No. In a game? 95% of the time Yes.

4-25
It seems as though one part of the definition pertains to an airborne player unable to release the ball on a pass or try.

The other part of the definition is, opponents hands firmly on the ball so that control cannot be obtained without undue roughness.

I'm going with a held ball prior to the travel here.

Since the player isn't airborne, you have to use the "other part," which states "hands". One hand isn't enough, IOW.

That said, always listen to bob.