When my trust issues a K1, do I just include it when the trust files the 1041? Also does the trust need to file K1 to beneficiaries which get no distributions?

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"When my trust issues a K1, do I just include it when the trust files the 1041?"

Yes. You are required to attach a K-1 that contains any income, deductions, or credits to your 1041.

See https://www.irs.gov/instructions/i1041/ch02.html#d0e6065

"Also does the trust need to file K1 to beneficiaries which get no distributions?"

No. However, it is generally considered a good practice to do so.