The best replacement for deposition is erosion.

The best alternatives to deposition are rated as following:
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★★★★  sublimation
★★★★  affidavit
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  decomposition
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  physical vapor deposition
  chemical vapor deposition

Your alternative for deposition is not listed? Suggest!
Speaking about deposition, one probably shouldn't forget about subpoena.

Other search terms related to deposition and their ratings are:
★★★★★ subpoena
★★★ erosion
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★ subpoena duces tecum
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Google Trends

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deposition
erosion
sublimation