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We consider triangular P\'olya urns and show under very weak conditions a general strong limit theorem of the form $X_{ni}/a_{ni}\to \mathcal{X}_i$ a.s., where $X_{ni}$ is the number of balls of colour $i$ after $n$ draws; the constants $a_{ni}$ are explicit and of the form $n^\alpha\log^\gamma n$; the limit is a.s.
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