Unless I'm mistaken, you're overthinking the "import" concept. I do think that your home instance caches info from communities you visit (MAYBE that influences what you see in all but I don't know really,) but otherwise there's no "importing" of anything. Otherwise, yeah the passport analogy isn't far off. You don't have an account on lemmy.ml, but it recognizes you as a registered user of lemmy.world and you get to interact as normal, you get tagged as @Swoggles@lemmy.world just like your passport says you hail from insert home country here. (I assume lol)

If you visit /c/aww@lemmy.ml for example, you're connecting to lemmy.ml as @Swoggles@lemmy.world. You're not bringing that community into lemmy.world, you're visiting it in lemmy.ml, as someone from lemmy.world (and as mentioned would appear if you comment as @Swoggles@lemmy.world. Because "visiting.") /c/aww@lemmy.world is just /c/aww on lemmy.world. It has zero at all to do with /c/aww on lemmy.ml, and they have zero at all to do with /c/aww on lemm.ee. All completely independent communities existing on different instances. There's no connections, no correlations, just somebody made /c/aww on lemmy.world, somebody also made /c/aww on lemmy.ml. They don't connect or anything. London, France has nothing to do with London, England, and /c/aww@lemmy.world has nothing to do with /c/aww@lemmy.ml.

Won't this model lead to like, heavy fragmentation of communities?

This is where people get lost coming from Reddit. Lemmy is not Reddit, and it isn't designed to be Reddit. Lemmy is designed to be a decentralized alternative, which offers far greater control at the cost of UX (usability, cohesiveness, whatever.) There aren't "single" communities, because that isn't what this is for. Decentralization is the point. Being able to (as one user put it) "make my own /c/aww with blackjack and hookers" is the point. That I can spin up a Docker container on my pi and build my own single user Lemmy instance as a home base, is the point.

It isn't meant or designed to provide a single central point of compilation, it's existence is for the exact opposite - Nobody has ultimate control because any one instance owner's power only extends so far as their server. The fragmentation everybody laments coming from Reddit actually provides redundancy, have you ever had a sub you like on Reddit get shut down for this that or the other reason? That's it, it's gone, sucks to suck. If you want more /c/aww, you CAN follow every /c/aww you can find - /c/aww@lemmy.world, /c/aww@lemmy.ml, /c/aww@lemm.ee, etc can ALL be in your sub feed. However, if @ruud (the owner of lemmy.world) decides he fucking hates adorable animals and nukes /c/aww@lemmy.world, you still have /c/aww on every other instance available.

This is the point that makes me mad about other Reddit exiles (not you.) They came to lemmy to leave a central authority, and got mad that there isn't a central authority. I try to point out that more 1 for 1 Reddit clones exist, but they get mad because that's "not what they want." Control and ease of use(the smooth singular experience of Reddit, Google, etc) are diametrically opposed. Either everything "just works" because everything is owned by and exists on Reddit servers, or you have to put in a little leg work to have control over your data etc because having control means I can get mad at lemmy.ml and block my server from federating with them, or I can tinker with the code and someone else's client doesn't understand what it's seeing, or any other number of things that can occur with the backend being in our hands vs a singular entity like a company. You just......can't have both, but Reddit exiles are mad about that. They want total decentralization of infrastructure and ownership, but want centralization of content, which just isn't possible without that single central pillar running the show (some people argue for communities that exist to scrape and clone every copy of a given /c/ across the fediverse to create a "supercommunity" but that just sounds like stealing with extra steps to me lol.)