AI image tools have got very good at generating beautiful compositions - but not all of them export files big enough to print. Midjourney, DALL·E 3 and Ideogram all now support high-resolution downloads that comfortably print at A3 and often A2.
The rule of thumb is 300 dpi at print size. A 2048 × 2048 px file is about 173 mm square at 300 dpi, so it prints crisply at A5, acceptably at A4 (around 250 dpi once cropped), and starts to soften from A3 upwards. For A3 you want roughly 3500 × 4900 px, and for A2 around 5000 × 7000 px. Use an AI upscaler (Magnific, Topaz, or the built-in Midjourney upscaler) to reach those sizes without visible pixelation.
Prompt for print, not for screens. Ask for 'poster', 'high detail', 'clean edges' and specify an aspect ratio that matches the A-series, which is 1:1.414 (√2) - not 2:3. Most tools accept 2:3 or 3:4 presets, so generate a little larger than you need and crop to 1:1.414 before uploading.
Finally - always order an A4 test print first if you plan to print a very large piece. It is cheap insurance against a £30 print you don't love.