Who gets posession?
 

Partner calls common foul on Blue #1... not in bonus.

Several seconds after whistle White #2 Shoves Blue #2... easy call for Dead Ball Tech.

Blue takes their two shots and then the table calls me over.

Blue #1 was added to the book at halftime...and no one told us.

Who gets possession after White shoots 2? Why?

Under NFHS, this has to be penalized when it occurs, not when it is discovered. To assess an administrative T, the foul would have to be enforced when the ball next becomes live; that is, at the start of the second half.

Blue gets two shots for white's T and the ball at the division line.

We've discussed this numerous times before, precisely because an unscrupulous scorekeeper could take advantage of this rule to benefit one team.

Too late on the scorebook issue, so that should simplify who gets the ball. White won't be shooting 2.

As Nevada notes, a shady scorer could take advantage of this by not telling the officials.

If the rule was different, a shady scorekeeper could hold on to that T until an opportune time and then inform the officials, giving their team possession and two extra free throws at a crucial time.

If you think the scorer is being shady, have him/her replaced. No T can be served, though.

It's more unscrupulous than not being told at all when the home team is the culprit?

The visitors have a book (or should). And, if the official has done his/her job, we can tell if a player has been added (assuming, I guess, that the home scoredr doesn't erase some entry and replace it with the "newly added" player)

I have ref'd multiple games this season, including college, where the visiting team doesn't have a book at the table.

That reasoning is pretty weak. Coach adds a name, team should get penalized. If he doesn't want the penalty to come at a crucial time, then don't hide the infraction. A scrupulous coach would volunteer, at the time of the infraction, that he/she just added a name to the book, and that would prevent an unscrupulous scorekeeper from pulling such a stunt.

But folks here make coaches responsible for correctable errors, something coaches have nothing to do with.

If the rule were written to penalize when discovered, coaches would be very motivated to be honest when adding names to the book.

Puppies already on the way...
 

Let's assume that the Administrative "T" was correct... who gets possession after the shots? The crew disagreement was over whether the "T"s were "simultaneous" because no time had come off of the clock between the two calls.

That's a fair point, and I have no idea whether my thoughts represent the reasoning for the way it's written now. Either way, there's an opening for shady.

Has it ever been recommended to the NFHS that admin T's should be POI.

Time coming off the clock has absolutely nothing to do with whether or not fouls are simultaneous.

Under NFHS you always administer in the order of occurrence. Blue shoots two for the white's intentional technical foul, white shoots two for blue's administrative technical foul, and then white gets the ball at the division line. Hypothetically for your situation, of course.

I'm sure it's come up, but NFHS likes to keep everything as simple as possible due to having officials across a wide spectrum of skill levels.

I would be fine with using POI for all T's in NFHS.

You dont know how depressing that statement is.

Not really, since NFHS rules are used for sub-varsity games and middle school games. I know they're technically written for varsity (uniform rules, for example), but penalty enforcement is going to apply all the way down to YMCA.

NCAA rules never have to be enforced by new officials (I'm not going to discuss idiotic rec leagues that use NCAA rules). I wouldn't be depressed about the fact that newer officials are joining every year. The rules are complicated enough for new officials who think they know them.