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I'd love to see charts with stats on percent of utxos by invoice address type (specially P2PKH, P2SH, P2SH-P2WPKH, P2WPKH, P2TR), over time; and same for percent of coin supply.

No doubt I can pay a company to access these numbers. Is there any alternative free as in free beer? I could pay my own time working my way through some open source software able to do this.

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While I think Pieter's answer provides exactly what you were asking for with the UTXO set repartition by output type, I think that you may also be interested in the Output Types by Count chart on transactionfee.info:

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The site has also more related charts that may be interesting in the context such as

and various charts for specific output types.

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You can find the first on https://txstats.com/dashboard/db/utxo-set-repartition-by-output-type?orgId=1. For a version weighed by value you can look at the graphs of the individual output types on the same site.

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