Hi Mary

The biologists might again provide more accuracy, clarity and detail than I can, but. . .

To answer your earlier question, I don't think that the centromeres of the X and Y recombine like the autosomes: the centromere forms part of the male-specific Y-chromosome (MSY) and does contain inheritable Y-SNPs. The centromere's DYZ3 region contains comprised of almost exactly repeating 171 base-pair sequences, grouped into 5.8 kbp higher-order repeats. This can't be easily read by short-read technology like Big Y, which only has read lengths of 100 base pairs, so each read only captures a fraction of one of these repeats, and it's impossible to securely tell in which one a SNP is found. Equally, like Y-STRs, the number of repeats will change between individuals - we don't yet know a lot about this kind of larger-scale variation, but it is slowly being uncovered by the T2T consortium.

That doesn't mean that there is no swapping of genes between X and Y. In addition to the pseudo-autosomal regions at the end of the Y chromosome, which do recombine with the X, there is substantial gene conversion between the two chromosomes. The most familiar part of this is the X-transposed region (the several-million-base-pair regions which represents the major difference between BigY-500 and BigY-700 tests), which our Y-DNA ancestor inherited from his X chromosome about two million years ago. However, gene conversion of much smaller units of a few hundred base pairs or less occurs frequently, notably in a few gene-conversion hotspots. The rate of conversion per base pair that of the rate of Y-SNP formation within these regions. This contributes to both "flaky" SNPs and poor mapping in parts of the Big Y test, and localised differences in the mutation rate (but these average out on large scales). There is a slippery rabbit hole of information here, which requires a steep learning curve and is definitely beyond my pay grade to say much more about!

For your recent question on the definitions of the telomeres and centromeres, this depends on the reference sequence that's used. Most of the time, we refer to the hg38 (or GRCh38) reference sequence, and this is what FTDNA, YFull, etc., now use as convention anyway. As I understand it, the pseudo-autosomal regions aren't telomeres in the strict sense, but parts of the X and Y chromosomes that retain their autosomal recombination. You can find them in YBrowse by typing in their names: PAR1 and PAR2. Similarly, the centromere can be found by typing in CEN and selecting chrY, which represents the centromere in the hg38 reference. Positions are listed in the search box.

Cheers

Iain