It may depend on whether or not the new series was canon, or the whether the two tv movies are canon.
Disclaimer: I don't know if these are the applicable processes under the laws.
If the new series is canon, JR's known assets may have been put in trust (including any possible inheritance from Miss Ellie),
with trust being administered by Bobby, who had power of attorney.
The transference may not be subject to inclusion in the Estate.
If so, the assets would pass to Bobby by the terms of the trust without being subject to the Estate.
JR could have had other accounts, life insurance, etc that automatically passed to beneficiaries.
Technically, not part of an Estate.
With regard to his business practices, JR must have been a good president, at least while Jock was alive, because Ewing Oil was making
healthy profits and growing. He taught the Oil business to Bobby, who later admitted
that JR had the ability to make some hard decisions ( decisions that Bobby
couldn't bring himself to make). The Asian wells may have been risky, but it did make the Ewings billionaires.
As the series went on, it could certainly be argued that JR took some unwise risks.