The source code below is generated using RetroMCP for version 1.2.5 unless otherwise stated.

Around line 340 of WorldGenBigTree.java, this can be found:
[code]
if(this.heightLimit == 0) {
this.heightLimit = 5 + this.rand.nextInt(this.heightLimitLimit);
}
[/code]
This code randomises the height of generated large oak trees. However, this height limit is set once due to the [code]this.heightLimit == 0[/code] check.

Line 51 of BiomeGenBase.java shows the generator instance being created: [code]protected WorldGenBigTree worldGenBigTree = new WorldGenBigTree(false);[/code] The instance is unique for every biome created and is used whenever a biome has large trees in it. Therefore, large tree heights are unique per biome. This is not too noticable however, since these trees only generate in forests, extreme hills, ice plains, jungles and plains.

Between Alpha v1.2.0 and Beta 1.7.3, BiomeGenBase still controlled what trees were generated, but it used a new large tree generator instance every time, as seen on line 64: [code]return (WorldGenerator)(var1.nextInt(10) == 0 ? new WorldGenBigTree() : new WorldGenTrees());[/code] In earlier versions, new generator instances were still being created with the exception that the height was shared per chunk: in Alpha v1.1.2_01, the following code was used around line 380 in ChunkProviderGenerate.populate().

[code]
Object var18 = new WorldGenTrees();
if(this.rand.nextInt(10) == 0) {
var18 = new WorldGenBigTree();
}
[/code]

In the image attached to this submission, it shows a world generated in Minecraft Java Edition 1.9.4. The red sand border shows the border between chunks generated before and after game reset. Trees with sea lanterns are large trees generated before the reset and trees with glowstone are large trees generated after the reset.

This bug has its own report on the official bug tracker:
https://bugs.mojang.com/browse/MC-11208