The gemara learns from the pasuk ולקחתם that one can only fulfill the mitzvah of taking the 4 species if it is "complete", meaning that he must have them all. However, the gemara qualifies this by saying that so long as he has all 4, the taking need not be "complete". Tosafos quotes a machlokes between the Be'hag and Rabbeinu Tam about what this means. The Be'hag says that one can fulfill the mitzvah even by picking up one after another, whereas Rabbeinu Tam says that they must all be picked up together just that they don't need to be bound together. Tosafos writes that according to all opinions it is still considered a beautification of the mitzvah to bind them together (as the gemara writes explicitly), but not necessary to fulfill the obligation (since we don't pasken like R. Yehuda). Rashi seems to hold like Rabbeinu Tam because he says that as long as you have all 4 "even if they aren't bound togehter" you are yotzei, implying that they must be lifted up together.
In Shulchan Aruch (651:12) the mechaber paskens like the be'hag that they don't need to be picked up together, not like rashi and rabbeinu tam. The Rama comments on this ובלבד שיהיו כולם לפניו (from the Rosh). The Sha'ar Hatziyun (67) cites a machlokes between the pri megadim and the gr"a why the Rama requires all four to be on the table in front of him. The Pri Megadim holds that one can fulfill his obligation so long as he owns all four at the time he picks up the first. The advantage of being all on the table in front of him is only in regard to the bracha so that he won't have to interrupt. However, the Gr"a explains that it isn't merely a consideration for the bracha but rather part of the requirement of לקיחה תמה that all 4 minim be in front of him and ready to be picked up at the time he picks up the first. According to the gr"a if one one a lulav here and an esrog in a different place he wouldn't be yotzei by picking up one and then the other, even according to the be'hag.