Runners 1st & 2nd, 2 out. Strike 3 is in the dirt as B1 swings & misses.
Catcher holds on to the ball- can B1 try to advance?
What if catcher does not hold on to the ball- is B1 out?

Was it an "uncaught (note that I didn't use the incorrect "dropped") third strike?" Yes.

Were there two outs, or was first unoccupied? Yes.

Conclusion: B1 can try for first, whether F2 now "holds on to the ball."

Are you asking if the ball hits the dirt and is caught is it a catch? The answer to that is NO. The ball was not caught and the batter can run.

#1 Yes, B1 may advance. Up to defense to either
tag B1, or throw ball to F3 at 1B for the out. Ball was
in the dirt.

#2 "Strike 3 is in the dirt", now does not matter
if catcher does of does not hold on to the ball, B1
only out if proper play may on him/her. Tag/or
throw to F3 at 1B

Conclusion: B1 can try for first, whether F2 now "holds on to the ball." [/B][/QUOTE]

B2 can try for first if he does not abandon his effort to reach it. I always wondered how an umpire determines if a runner has abandoned his effort. Does he need at least one foot in the dug out to be considered abandoning his effort? What if he only sticks an are in the dug out and the realizes that he can go back? Do you call him out at this point? Or do you call him out when he begins to walk droopingly towards the dug out?

The FED rules do not say "abandon his effort to reach it." THey say, "gives up by entering the bench or dugout area." 8-4-1i. To enter dead ball territory in FED, you must not have a foot in live ball territory.

You don't say what level of baseball. If it's LL, Majors or below, batter's out.

Bob