Don't know what the end point is but I were to guess it would be when the species is completely 'deprotonated' or 'protonated' based on whether you add base to a highly acidic solution or if you add acid to a highly basic solution respectively. The equivalence point would be when the species exists as 'zwitterions' mostly, i.e., no charge. Half equivalence would be as you described above. Buffers are prepared at Half equivalence point. Sorry if this does not help. And off course let me know if I am wrong....
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