Read the imaging carefully. A swollen pelvis with thinned cortex but a completely normal ureter localizes the block to the pelviureteric junction. That single fact sets the diagnosis as PUJ obstruction.
The next question is whether to save or sacrifice the kidney. Split function sits at 19 percent, which is depressed but still meaningful. The accepted threshold for abandoning a kidney is roughly 10 percent or less, so at 19 percent the organ deserves a reconstructive attempt rather than removal.
The operation that corrects PUJ obstruction and reconnects a wide, draining junction is the Anderson-Hynes dismembered pyeloplasty. It excises the stenotic segment and restores funnel-shaped drainage, giving the kidney its best chance to recover.
The alternatives fall away. Nephrectomy is for a kidney functioning under about 10 percent, not this one. A nephrostomy gives only temporary external drainage and cures nothing. Endopyelotomy performs poorly in children with grossly dilated systems. Pyeloplasty is therefore the definitive answer.
\[\boxed{\text{Pyeloplasty}}\]