A B+ tree is the index under almost every database table. Keys live only in the leaf pages at the bottom; the levels above are a slim directory of separators. Each node holds up to d children — the fanout — so the tree stays wide and short.
When a page overflows it first tries to nudge a key into a neighbour with room; only when the neighbours are full does it split in half, and that split can cascade upward and split the root — the one moment the tree grows a level. Sorted keys always pile onto the last page, which has no right neighbour, so it splits and seals every left page at half full: the classic sequential-insert waste. Scattered keys land everywhere and top pages off to ~90%.
Height grows with the logarithm of the key count, so a three-level tree at a realistic fanout indexes hundreds of millions of rows — and a lookup reads exactly one page per level. That is why a database can find one row among a billion in a handful of disk seeks.
The simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.