Synthetic or semi-synthetic minimal cells are those cell-like artificial compartments that are based on the encapsulation of molecules inside lipid vesicles (liposomes). Synthetic cells are currently used as primitive cell models and are very promising tools for future biotechnology. Despite the recent experimental advancements and sophistication reached in this field, the complete elucidation of many fundamental physical aspects still poses experimental and theoretical challenges. The interplay between solute capture and vesicle formation is one of the most intriguing ones. In a series of studies, we have reported that when vesicles spontaneously form in a dilute solution of proteins, ribosomes, or ribo-peptidic complexes, then, contrary to statistical predictions, it is possible to find a small fraction of liposomes (<1%) that contain a very large number of solutes, so that their local (intravesicular) concentrations largely exceed the expected value. More recently, we have demonstrated that this effect (spontaneous crowding) operates also on multimolecular mixtures, and can drive the synthesis of proteins inside vesicles, whereas the same reaction does not proceed at a measurable rate in the external bulk phase. Here we firstly introduce and discuss these already published observations. Then, we present a computational investigation of the encapsulation of transcription-translation (TX-TL) machinery inside vesicles, based on a minimal protein synthesis model and on different solute partition functions. Results show that experimental data are compatible with an entrapment model that follows a power law rather than a Gaussian distribution. The results are discussed from the viewpoint of origin of life, highlighting open questions and possible future research directions.