The best replacement for tener is haber.

The best alternatives to tener are rated as following:
★★★★★  haber
★★★  estar
★★  tener que
★  hacer
  deber
  haber spanish

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Speaking about tener, one probably shouldn't forget about expressions.

Other search terms related to tener and their ratings are:
★★★★★ expressions
★★★ preterite
★★★ que
★★ idioms
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Google Trends

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tener
haber
estar