8:51 AM PT -- In a statement released Tuesday morning, Oliverson's family said the baseball player is showing positive signs of recovery.
"Just 36 hours ago, Easton was 30 minutes from passing away," the family said. "Now 36 hours later, he has a team of Trauma 1 doctors who are in absolute awe of his tremendous progress."
"One of his doctors said that everything they have hoped Easton to be able to do in the last 12 hours, he has done and more."
The family is asking for continued prayers.
A 12-year-old baseball player gearing up to compete in this week's Little League World Series in Pennsylvania is now fighting for his life -- after he fell from a bunk bed at the Williamsport venue's dormitory complex over the weekend.
Easton Oliverson -- who pitches and plays outfield for the Snow Canyon Little League team that's making its first-ever LLWS appearance this month -- sustained a fractured skull in the incident Sunday night, according to his uncle, Spencer Beck.
Beck tells TMZ Sports ... Oliverson was sleeping on the top bunk, when he suddenly fell out of the bed and hit his head. He was immediately rushed to the hospital, where he underwent emergency surgery.
Beck tells us Oliverson, who's earned the nickname "Tank," is currently in a medically induced coma -- though he and the rest of the family are optimistic the boy will make a recovery.
"He's a really good kid, very loving," Beck said. "Full of smiles. Just a fun, fun kid -- so we're all praying for him."
Little League officials released a statement Monday regarding Oliverson's condition ... saying, "At the request of his family, Little League International encourages all to join us in keeping the Snow Canyon Little League player and his family in our thoughts and prayers, as we wish for a full and complete recovery."
"Little League International will continue to use all available resources, including those provided by UPMC in North Central Pa., through the Player Wellness Center, to support the player, his family, and his coaches and teammates, as we navigate this unfortunate situation."
Oliverson's team, meanwhile, said it will still compete in its first game of the World Series in Williamsport on Friday -- writing in a statement that Oliverson's father, who's a coach on the squad, wanted them to continue onward in the tournament.
"While our hearts are heavy," the team said in the statement, "we are committed as a team to have an opportunity to take part in something that is only dreamt about by others."
Beck tells us the family has set up a Venmo account for Oliverson -- @MiraclesForTank -- to help with medical expenses.
Originally Published -- 7:37 AM PT